We investigate an electron interacting with a non-relativistic quantum field in the semiclassical regime, where the field behaves classically while the particle remains quantum. In this setting, we derive an approximation for the solution of the time-dependent linear Schrödinger equation in terms of simpler semiclassical states. These states are governed by the Schrödinger-Klein-Gordon equations, a system of two coupled non-linear PDEs that describe a particle interacting with a classical field. We present results for two models: the Fröhlich polaron and the renormalized Nelson model. After a detailed discussion of the models and results, we will briefly outline the proof, which relies on a nonlinear adiabatic theorem and a careful analysis of the fluctuations around the semiclassical states. The talk is aimed to be accessible to non-experts and is based on joint work with M. Brooks, N. Leopold, S. Rademacher, B. Schlein, and R. Seiringer.