What Can we Learn from the Solution to the Quantum Rabi Model?

The Rabi model is a fundamental model in the study of quantum optics introduced by Rabi in 1937, which was recently solved analytically (Braak 2011). We review different methods to solve dynamical problems in quantum optics, and we explore how they can be applied to specific quantum optical models. These solution methods leads us to consider symmetries and limiting cases of these models.