The development of the latter and the study of the physical scenarios induced by strong correlations are therefore both of great importance. In this context, I will present the results of my numerical investigations of strongly correlated systems: specifically, i) the equilibrium and out-of-equilibrium physics of a class of bosonic Hubbard models with extended-range interactions, relevant for cold atom experiments, as well as ii) the ground-state properties of the fermionic t-J model, a candidate Hamiltonian to describe high-T_c superconductivity, in the presence of two mobile holes. Path Integral Monte Carlo simulations and a Tensor-Network-based variational approach have been chosen as numerical techniques for the two problems, respectively. The main results I will discuss are the demonstration of an out-of-equilibrium superglass state in the bosonic scenario, obtained in the absence of frustration sources in the system, and of a d-wave hole bound state in the t-J model. My investigation of the latter in the 2-hole case is foundational for the application of my approach of choice to other problems, of direct interest for high-T_c superconductivity, where the physical picture is still unclear (such as the t-J model at finite hole density). I will finally illustrate my work on Diagrammatic Monte Carlo, a recently introduced technique for the study of strongly correlated systems of fermions and frustrated spins.