I will discuss the role of dynamical correlations in predicting electronic excitation spectra in systems ranging from molecules to condensed systems with thousands of electrons. Using the many-body perturbation theory based on Green's function formalism, we can study individual quasiparticle states and even non-trivial quasiparticle-quasiparticle interactions. First, I will exemplify these approaches on small test systems, for which we can find numerically exact excitation spectra and study the role of various theoretical formulations. Second, I will show practical applications to quantum materials, e.g., in studying the correlated phenomena for localized moire states in twisted bilayer graphene. For the latter, we employ our real-space and real-time stochastic methods and combine them with embedding and ab-initio downfolding onto explicitly correlated Hamiltonians. This framework, leveraging efficient low-scaling numerical techniques, is generally applicable to (quantum) material science and chemistry problems and constitutes an ideal platform for simulating complex nanoscale systems with thousands of electrons at a minimal computational cost.