When I was at Berkeley, the framework of quantum field theory could calculate the dynamics of electromagnetism. It could roughly describe the motion of the weak nuclear force, radiation. But it hit a brick wall with the strong interaction, the binding force.
In the lab, we could not see or physically describe the mathematical objects that we called quarks, which we suspected were the key to unlocking the dynamics of the strong force that binds together the clump of protons and neutrons at the center of the atom.