There are, as Lee Smolin writes in his book The Trouble With Physics, five major problems in theoretical physics. First, the unification of the four forces and second, the reconciliation of general relativity and quantum mechanics. These two problems are perhaps interdependent: to solve one we need to solve the other. Next, the third problem is about the Standard Model. Although most of us believe it to be the most successful theory there is, it has a lot of constants with values we don't know the origin of. We can experimentally find the values, but we don't know why these constants have to take on those particular values. There are some other problems as well. The fourth problem is about dark matter and dark energy. We know very little about them, and they were postulated simply to explain away some crazy cosmological observations which couldn't be explained by our current theories. The last problem is, according to me, the most important problem in all of science. Making sense of quantum mechanics. The quantum measurement problem. A theory of everything, to be really a theory of everything, must solve each of these problems.
So what is a theory of everything? It's simply a theory that would explain all possible interactions in Nature in a single theoretical framework. And probably solve all the five problems discussed above. Our universe is dynamic, and everything in it is changing. As you may know, force causes this change. Force can change the state of motion, direction and configuration of an object. There are many different forces, but often many forces are just different forms of the same fundamental force. Over the years, physicists have come to the conclusion that there are four fundamental forces. One, the gravitational force. Second, the electromagnetic force. Third, the weak nuclear force and finally, the strong nuclear force. These forces can pretty much explain every interaction that can possibly take place in our universe. Just think about it. All the possible interactions. Physicists today are trying to unify these four forces into a single theoretical framework. Then, in a single theoretical framework, we could explain all the interactions that can take place in this universe. Such a theory is what we mean by a theory of everything.
First, let us discuss gravity. Gravity here is the odd one out, because all the other forces can be explained in terms of exchange of certain fundamental particles. But we haven’t yet discovered such a particle for gravity. Today, most physicists see gravity as a force arising out of the curvature of spacetime. Albert Einstein, in his theory of relativity, proposed that matter and energy are basically the same thing, and so are space and time. The presence of matter/energy can curve the spacetime around it. And this curvature of spacetime affects the movement of the bodies present around. So in this view, two bodies are not exactly pulling each other. They are moving toward each other due to the curvature of spacetime. But recent discoveries, like gravitational waves from two colliding black holes, hint at the existence of gravitons (the force-carrying particle for gravity). And general relativity doesn't rule out gravitons, and it is thought by many that gravitons are extremely likely to exist. Gravitational waves might be made up of these gravitons (in much the same way light waves are made of photons).
It should be noted that although general relativity has survived many stringent experimental tests, it breaks down inside a black hole or at the Big Bang. This only shows that general relativity is not a complete theory, and there is a deeper, all-encompassing theory which would account for dark matter, dark energy (etc.) naturally, unlike general relativity. Quoting Celia Escamilla-Rivera from this Quanta Magazine article, "The problem is that general relativity is not general enough. If you want to explain dark energy, this invisible energy that seems to be accelerating the universe’s expansion, you need an extra component in the equation, called the cosmological constant. This extra component doesn’t exist naturally in general relativity; you need to add it by hand." Please keep in mind that dark matter and dark energy are simply terms we have coined to phenomena which can't be explained at present. It is surely possible that we will discover some deeper theory in the future which would explain these phenomena, or shed light on what problems with our current theories have given rise to the misconception of the existence of these phenomena.
When Einstein was busy fighting his battle in the thickets of spacetime, other physicists were developing a new and revolutionary theory: quantum mechanics. (It should be noted that Einstein himself also played an important role in the development of quantum mechanics, although he later refused to accept quantum mechanics as a complete theory.) Quantum theory was born when Max Planck showed that energy can't be radiated continuously, but in discrete packets called quanta. This was an essential step in resolving the ultraviolet catastrophe. Planck showed that the energy is directly proportional to the frequency, and thus is equal to a constant multiplied with the frequency. This constant is what we call Planck's constant. It was Einstein's insight that to explain the photoelectric effect, we must think of light as a stream of discrete quanta, called photons. Einstein reintroduced the particle nature of light, and it was necessary. Today, we say that light has dual nature: the wave theory explains some phenomena while you need the particle theory for some other phenomena. Then we had Louis de Broglie's great idea that just like light (supposed to be a wave) has dual nature (particle nature in addition to wave nature), matter (supposed to be of particle nature) has a wave nature too. This has been verified by studying the diffraction of electrons, and has wide ranging applications, like the electron microscope. The electron was thought of as a point-like particle. Then quantum theory proved that the electron, and in fact everything else, has a wave nature too. Werner Heisenberg showed that it was impossible to determine both the position and momentum of a particle simultaneously. There is a certain amount of uncertainty in Nature. Then came Schrödinger's equation. There was the interpretation of the wave function as a function the square of which gives the probability of finding the particle in the given region. Only on observing the particle, does the wave function 'collapse' to a distinct 'value,' and we observe the particle in a distinct location. Before observation, the particle has a non-zero probability of existing everywhere, even in distant galaxies. (Here I'm referring to the quantum measurement problem, and there are a lot of philosophical difficulties here. According to quantum mechanics, before a measurement or observation is made, an object exists in a superposition of all possible states, and in multiple places at the same time. Only on observation does it collapse to a distinct state. While it is not clear whether this observation requires consciousness (likely no), it is known for sure that measurement must be made for things to exist in a distinct state. There are some other interpretations like the many-worlds interpretation which says that the wave function never collapses. All the possibilities take place in different alternate, parallel worlds.) And, roughly speaking, Nature tries out all possibilities, so if we wait long enough, we can observe the effect of quantum tunneling: the particle can instantaneously disappear from here and appear in a distant location. Tunneling has been observed already. But don't expect we will be walking through walls any time soon! Anyway, quantum mechanics disproved all common sense notions about reality. In this new world, a particle can simultaneously pass through two slits, you have a certain probability of tunneling to a distant galaxy (although not in your lifetime, such extremely rare events will occur after a long, really long time) and you get the idea. There is a certain amount of randomness in Nature and everything is reduced to probability, in some sense. Some physicists accepted this revolution, while others were not so happy about this. (Note that although I say there is a certain amount of randomness in Nature, more appropriately, according to quantum mechanics, either the outcomes of quantum events are entirely random or the outcomes of quantum events are actually deterministic deep down, and we perceive them to be random due to our limitations. I think the universe might be deterministic deep down, and it appears random and probabilistic to us due to our limited knowledge and incomplete understanding of it. The reason I say the universe might be deterministic is that even randomness can be deterministic. There are laws that apply to random systems; random doesn’t mean it can’t be studied or understood. All I mean by deterministic is that the universe functions according to some universal laws. However, as pointed out by one of my readers recently, I have claimed that ordered complexity is a fortunate product of random processes. How do I reconcile this with my belief that the universe might be deterministic deep down? Well, to be honest, right now we don’t have enough knowledge to determine whether these two statements are conflicting. And when I say ordered complexity is a fortunate product of random processes, I simply mean that everything happened spontaneously and not because of some greater power or God. But I don’t think this rules out the possibility of a deterministic universe. Notice the phrase “ordered complexity”. Ordered implies that certain rules are being followed, and thus determinism may hold.)
Now, we all know what a charge is. It is an intrinsic property of some particles, and the electron carries the smallest amount of charge that can exist independently. The electron carries a charge which is in nature very different from the charge carried by protons. There are two types of charges, positive and negative and unlike charges attract one another while like charges repel one another. This attraction and repulsion fall under the electromagnetic interaction. This attraction holds the nucleus and electrons in an atom together. The strong nuclear and weak nuclear forces operate on a much smaller scale and hold the nucleus of the atom together. These three forces are all caused by the exchange of fundamental particles called bosons. There are two types of fundamental particles. Bosons, which give rise to forces, and fermions, which make up the matter. At this point, it should be noted that the unification of even just these three forces was not easy. After Einstein published his geometrical theory of gravity, he, along with many other scientists, started looking for a geometric interpretation of electromagnetism. The weak nuclear and strong nuclear forces were not known at that point. It was soon discovered, by Theodor Kaluza (and his theory was later improved by Oskar Klein), that the existence of an extra, hidden dimension can account for electromagnetism in a world which is consistent with Einstein's general relativity. In other words, Kaluza, as Lee Smolin writes in The Trouble With Physics, "applied Einstein's general theory of relativity to a five-dimensional world and found electromagnetism." Smolin further writes, "gravity and electromagnetism [were] unified in one blow, and Maxwell's equations are explained as coming out of Einstein's equations, all by the simple act of adding a single dimension to space." The weak and strong nuclear force can also be, in some sense, unified with gravity and electromagnetism by adding even more dimensions. But why don't we see these dimensions? The response was that these dimensions are curled up to very small lengths and we can't perceive them. These dimensions are so small that even atoms are not able to enter these dimensions. However, there are a lot of problems with Kaluza-Klein theories, and ultimately these theories were shown to be incorrect.
The best candidate we have for a theory of everything is, perhaps, string theory. If string theory turns out to be correct, then the correct question about the final theory should be asked in terms of strings. String theory proposes that one dimensional ‘strings,’ the different modes of vibrations on which correspond to the different particles, are the most fundamental building blocks of the universe, and no particle is any more fundamental than any other particle. In string theory, forces arise from the joining and breaking of strings. All forces and particles can be explained by assuming strings propagate in a fixed background in such a way so as to minimize the area taken up. String theory basically replaces the idea of zero dimensional point particles with the idea of a one dimensional string of energy. Interestingly, string theory was initially developed as a theory of the strong nuclear interaction. But then it was discovered that string theory includes all the three forces plus gravity. The latter, as a requirement, must be included for the theory to work. (Gravitons, according to string theory, arise from the vibrations of only closed strings.) This suggested that instead of just describing the strong nuclear interaction, string theory is in fact the theory that unifies all the four forces of Nature. There were problems, however. Some string theories predicted the existence of faster-than-light particles called tachyons which rendered the theories unstable. Okay, tachyons can be eliminated by using supersymmetry. But string theory requires twenty-five spatial dimensions and one time dimension to work. After supersymmetry was incorporated into string theory, we could reduce the number of required dimensions to ten (nine spatial dimensions). The explanation was that these dimensions are curled up to such small lengths that they are not perceivable. But, as Smolin writes in The Trouble With Physics, "This gave rise to great opportunities, and great problems... earlier attempts to use higher dimensions to unify physics have failed, because there were too many solutions... It also led to problems of instabilities, because there are processes by which the geometry of the extra dimensions unravels and becomes large and other processes whereby it collapses to a singularity." More problems remained, and new problems came up as string theory developed. There was still excitement, for it was proved that string theory is finite and consistent. All the previous quantum gravity theories were not finite and consistent. String theory promised to be a ray of hope. String theory is beautiful and elegant. But we must also remember that beautiful theories have failed before. And then it was discovered that string theory is not a unique theory. Five different versions of superstring theory were discovered. The hope was that all these theories are different manifestations of some deeper, underlying theory. And we have evidence that such a theory - M-theory - actually exists, but we haven't been able to work out the details yet. There is one more problem with string theory. String theory is background dependent. We describe strings moving in a fixed background, in fixed space and time. But general relativity is background independent. And as far as we know, a final theory must also be background independent. Background independence requires that, quoting from Wikipedia, "the defining equations of a theory to be independent of the actual shape of the spacetime and the value of various fields within the spacetime. In particular this means that it must be possible not to refer to a specific coordinate system - the theory must be coordinate free. In addition, the different spacetime configurations (or backgrounds) should be obtained as different solutions of the underlying equations." The background must be derivable from first principles, and not be fixed. As is explained in the Wikipedia article, we must not increase the number of inputs the theory needs to make its predictions. Well, string theorists assume the background to be almost fixed with small disturbances, and use perturbation techniques to account for these disturbances.
There are alternatives to string theory. The best alternative being loop quantum gravity which attempts to apply the principles of quantum mechanics to gravity. General relativity, as we know, describes gravity as a consequence of the curved geometry of spacetime. Loop quantum gravity, however, suggests that space itself is discrete, quantized and granular (not continuous). Loop quantum gravity makes some testable predictions, and may also be a successful, finite and consistent theory of quantum gravity. And loop quantum gravity is background independent as well. Loop quantum gravity assumes that space is emergent from discrete building blocks. It indeed may be the case that gravity, space and time are emergent from some deeper structure. If you're interested in learning more, take a look at this. Also, note that even string theory suggests spacetime is emergent, but it is a different kind of emergence. This is explained beautifully in this Scientific American article: "Although string theory and loop quantum gravity both suggest that spacetime is emergent, the kind of emergence is different in the two theories. String theory suggests that spacetime (or at least space) emerges from the behavior of a seemingly unrelated system, in the form of entanglement. Think of how traffic jams emerge from the collective decisions of individual drivers. The cars are not made of traffic—the cars make the traffic. In loop quantum gravity, on the other hand, the emergence of spacetime is more like a sloping sand dune emerging from the collective motion of sand grains in wind. The smooth familiar spacetime comes from the collective behavior of tiny “grains” of spacetime; like the dunes, the grains are still sand, even though the chunky crystalline grains do not look or act like the undulating dunes." The idea that spacetime is emergent is speculative and somewhat ill-defined. We understand very little about it. But I think there is some good evidence suggesting that there is an underlying structure, from which space and time may be emergent.
Anyway, the problem with string theory is that we don't fully understand it yet. And also, there is no concrete experimental support for it. String theory has made no unique and viable prediction. The predictions of string theory, if proved to be true, will not conclusively prove that string theory is true. And even if these predictions are false, string theory might still be true. Also, string theory involves so complicated mathematics that we don't even know what the exact equations of the theory are. We know only approximations, which have been partially solved. But that's no reason to lose hope. Physicists have every reason to believe that they are on the right track! But at the same time, it is important to remain skeptical until we have enough experimental evidence. Science is about the real world. Beautiful theories need not be true.
In the end, I would like to say that some people believe that once we find a theory of everything, physics would come to an end. Of course not. We have just started unraveling the mysteries of the universe, and there are more surprises in store for us. If you would ask me whether I believe we are going to find the theory of everything, I would say maybe yes, in the course of time. String theory and loop quantum gravity are promising approaches, and eventually I believe we would discover the final theory. We will definitely discover something. I have this gut feeling that near-future discoveries in physics will be changing the way we see the world. A final theory is definitely possible, but we don’t understand the problems well enough yet, so it is not possible to comment on how far away the solution is.