Enhanced electron-electron correlations in quantum materials often play a central role in giving rise to exotic many-body phenomena, among which the Mott phase transition is a paradigmatic example. Once a quantum material is driven out of equilibrium by an ultrafast optical pulse, the resulting dynamics is governed by a complex and highly interdependent interplay of its internal degrees of freedom. These include the charge, spin, orbital, and lattice components of the system, each of which evolves on characteristic timescales ranging from femtoseconds to picoseconds. The collective modes in correlated systems are particularly interesting, since they involve the coherent response of many particles, and thus cannot be captured within simple single-particle frameworks. Based on (nonequilibrium) Green’s functions, the dynamical mean-field theory (DMFT) and its nonequilibrium extension offer a powerful framework for studying strongly correlated systems in high dimensions. This thesis focuses on the application of ab initio density functional theory + nonequilibrium DMFT approach to the study of charge dynamics and dynamical phase transitions in a range of realistic materials exhibiting strong electronic correlations. Additionally, we explain how to investigate nonlinear responses and collective excitations in correlated materials using the multi-dimensional coherent spectroscopy signals.