Quantum systems with strong interaction exist in many branches of physics and present a challenge for theory. We will discuss some recent methods to solve the problem, focusing on one  particular example: the fractional quantum Hall fluid. Many phenomena occurring in this fluid can be explained by postulating a new type of quasiparticle - the composite fermion. I will describe theories of this composite fermion, in particular the recently proposed "Dirac composite fermion theory", and how research in condensed matter physics has stimulated the discovery of a large number of new dualities between quantum field theories, previously unknown to high-energy physics.