Modern computational chemistry strives to provide an atomistically detailed dynamical description of fundamental chemical processes. The strategy for reaching this goal generally follows a two-step program. In the first step, electronic structure calculations are used to obtain the force fields that the nuclei are subject to. In the second step, molecular dynamics simulations are used to describe the motion of the nuclei. The first step is always based on quantum mechanics, in the light of the pronounced quantum nature of the electrons. However, the second step is most often based on classical mechanics. Indeed, classical molecular dynamics simulations are rroutinely used nowadays for describing the dynamics of complex chemical systems that involve tens of thousands of atoms. However, there are many important situations where classical mechanics cannot be used for describing the dynamics. Our research targets the most chemically relevant examples of such processes.