Particles confined in reduced dimensions (less than 3) exhibit new and often surprising behavior and phenomena, especially in the quantum regime and at low temperatures (from fractions of Kelvin to fractions of microKelvin).  In this situation, the effect of interparticle interactions (correlation) becomes very important and accurate measurements are crucial in order to understand and predict, in quantitative terms, the exotic properties of systems realized in the laboratory. We study electrons confined in solid-state semiconductor devices (1 and 2D electron systems) and more recently ultracold Fermions in magnetic traps. We employ quantum Monte Carlo simulations and many-body approximations, techniques in which we have longstanding expertise