The answer to the question is yes. The framework of quantum field theory allows one to describe all interactions except for gravity. Different realizations of QFT take account for different fields of physics: For example, phenomena of electromagnetism are described accurately by quantum electrodynamics, while the strong interaction that describes how nuclei behave is covered by quantum chromodynamics. Together with the theory of weak interactions, these two theories form the Standard Model of Particle Physics. Apart from particle physics, there also exist quantum field theoretic approaches towards condensed matter physics.
The problem with a fundamental quantum field theory of gravity is that when one naively starts from general relativity and tries to quantize it, one runs into the difficulty of nonrenormalizability. This means that one encounters divergent integrals that cannot be removed by modifying the theory, making the theory useless. One solution to this problem may be approaching the issue from a different perspective and use the framework of string theory.
The reason why quantum field theory is successful is the fact that at high energies and small distances, nature is dominated by both relativistic and quantum mechanical effects, and quantum field theory can be seen as a unification of special relativity and quantum mechanics.