We shall present our recent investigations on quantum dynamics in pumped hybrid quantum systems. Initially, we will discuss the performance of a quantum heat engine consisting from many three-level quantum emitters collectively interacting with the cold and hot baths, respectively. We have found that the performance may be enhanced considerably in a Lambda-type ensemble compared to a V-type one. Then, we turn to an optomecanical setup where we demonstrate multi-phonon effects in dispersive regimes of interaction. We shall finalize by discussing the entanglement creation in a pair of laser pumped two-level qubits and its relationship with cooling effect of the boson mode which is coupled to them. We demonstrate that the entanglement occurs even for resonance laser-qubit interaction - an effect arising due to the presence of the dipole-dipole interaction among the two-level qubits.