After the completion of quantum theory in the twenties, during the following decades came relativistic quantum field theory. Quantum field theories, which encompass our present understanding of matter, combine special relativity and quantum theory. In this framework, the difficulties with the philosophically problematic sides of quantum theory have seemingly faded away. Quantum field theories, which can be conceived as quantum mechanics in the case with an infinite number of degrees of freedom, have proven to be extremely successful.
The world is presented as consisting of quantum particles that constitute both matter and radiation. All structure and all changes in the world are due to four forces or interactions. The atoms are held together by the electromagnetic interaction, and within the nucleus there are the strong and weak forces acting. The strong force acts on the protons and neutrons, keeping together the quarks that they are made of. Without the strong force there would be no atomic nucleus, and the universe would consist of a porridge of leptons, like the electron, and quarks. The electromagnetic and gravitational forces have an unlimited range, contrary to the nuclear forces. Gravitation is the only all-embracing interaction, and the only one that has not been formulated as a quantum field theory.
When applying quantum mechanics to gravity, one is in a way applying it to space and time. A quantized version of gravity would then be a quantum theory of the very structure of space and time. But the all-embracing gravitation interacts with every form of energy, also with itself. This makes theory nonlinear, which means that it is impossible to superimpose gravitational processes. This gravitational nonlinearity complicates the procedure of quantizing theory, since it makes it difficult to identify a suitable Hamiltonian for quantum gravity.
Nature has however already solved the problem. The world at bottom is a
quantum world. Nature does not start out with a classical theory which is
thereafter quantized. The problem is that 
live in a classical world
and none of us knows how to get a quantum theory without starting
out from a classical theory.
Like every dynamical theory, also quantum field
theories are therefore based on classical mechanics.