The project is divided in two parts. First, we aim at investigating the physics of strongly correlated electronic systems. We have developed an Auxiliary Field Quantum Monte Carlo code which allows us to solve numerically many models relevant to describe the main features of several materials including superconductors, diluted magnetic semiconductors, Mott insulators etc.... Second, we aim at studying the electronic structure of small transition metal complexes through Diffusion Monte Carlo simulations, performed using the Casino code. Unfortunately, for such molecules, 'standard' electronic structure techniques (Density Functional Theory and Hartree-Fock) fail in predicting the correct magnetic ground state and more accurate and computationally expensive quantum chemistry methods are required. Our results will provide new insights into the physics and chemistry of these systems.