First of all what is “domestication”?
Domestication is an evolutionary process. It is the evolution of new species (e.g. dogs) as a result of one species (e.g. humans) selecting other species (e.g. wild wolves) based on certain traits and intervening in the evolutionary process through artificial selection by allowing only those with those traits to mate and not allowing others to mate (or even actively killing or driving them away). In this way, animals can become "domesticated", that is, "fit for home", by differentiating themselves from their ancestors, who could be predatory and wild.
The process of behaviorally acclimating an animal to live and shelter partially comfortably in human situations is known as taming. Although the animal is not tamed, it is capable of coexisting with people. There is learning rather than evolution during domestication. Evolution and learning go hand in hand with domestication. A crow that approaches you without hesitation because you feed it, for instance, is tamed but not domesticated.
On the other hand, not all domesticated animals have to be tamed. Many animals that we have shaped through artificial selection in the evolutionary process are actually not domesticated. The best example of this is chickens. Chickens are species that have changed significantly through artificial selection applied by humans in the evolutionary process; however, they are still not domesticated animals, and they do not like to come close to humans and their houses and live directly with them.
Strictly speaking, we don't know the limits of domestication at the moment. Practically speaking, we're not even sure if there's an animal that can't be domesticated, because we've managed to tame every animal we've ever laid our hands on in one way or another. What's more, we now know that many animals have an incredibly high potential to evolve, so it's often possible to shape them through artificial selection. But the fact remains that some animals are much easier to tame than others. The reasons for this can be summarized as follows:
Fast growth rate, Stubbornness / Flexibility, Sociability, Acting with a Group Mind etc. In fact, all of these are controllable traits that can be brought about in a species by evolution through artificial selection. The animals we want to domesticate don't necessarily have to have them all together.
Of course, evolution by artificial selection has historically often occurred in combination with, or following, natural selection. The evolution of cats and dogs, for example, probably did not involve humans actively searching for wild cats and wild dogs in the wild, finding them, bringing them to their camps and breeding them by artificial selection. Rather, wild cats and dogs began to live near human habitats for a variety of reasons (easier foraging, refuge, shelter, protection, etc.). This is the natural selection part. However, as humans interacted with these animals, they realized that they could benefit from them and began to mate the ones that suited their needs and expel the others. Thus, over generations, domesticated forms evolved from wild forms. Today there is practically no resemblance between a wolf and a Chihuahua or a wild cat and a Scottish. This radical change is one of the clearest proofs of evolution.
Of course, not only cats and dogs have been domesticated. Wild animals that humans have managed to domesticate include sheep, pigs, goats, cattle, chickens, donkeys, ducks and many more.
As a result, it is theoretically possible to domesticate every living thing. As long as evolution exists, it is theoretically possible to dominate it. As long as life exists, evolution must exist, so domestication is automatically a possibility. So maybe one day your grandchildren will keep a wild animal that you love at home. The thought is very exciting!