Quantum to classical crossover in cavity QED and optomechanical systems Modern cavity QED and cavity optomechanical systems realize the interaction of light with mesoscopic devices which exhibit discrete (atom like) energy spectra or perform micromechanical motion. In this thesis we have studied the crossover from the quantum regime to the classical limit of two prototypical models the Dicke model and the generic optomechanical model. The physical problems considered in this approach range from a ground state phase transition its dynamical response to general nonequilibrium dynamics including Hamiltonian and driven dissipative chaotic motion. The classical limit of these models follows from the classical limit of at least one of its subsystems. The classical equations of motion result from the respective quantum equations through the application of the semiclassical approximation i.e. the neglect of quantum correlations. The approach of the results from quantum mechanics to the prediction of the classical equations can be obtained by subsequently decreasing the respective scaling parameter. In order to obtain exact results we have utilized advanced numerical methods e.g. the Lanczos diagonalization method for ground state calculations the Kernel Polynomial Method for dynamical response functions Chebyshev recursion for time propagation and quantum state diffusion for open system dynamics. We have studied the quantum phase transition of the Dicke model in the classical oscillator limit. Our work shows that in this limit the transition ... Quantenphasenübergang Quantenoptik Optomechanik cavity QED optomechanics quantum phase transition nonlinear dynamics