Electron glasses are disordered systems of localized electrons with long-range Coulomb interaction, as found at low temperature in doped semiconductors, amorphous semiconductors, and granular metals. Experiments on several of these systems demonstrate a very slowly relaxing conductivity and striking non-equilibrium effects that suggest glassy physics of electronic origin. I will review our recent studies of the electron glass problem, mostly based on large-scale numerical computations, addressing the existence of a thermodynamic glass phase, the shape of the Coulomb gap in the single-particle density of states (which affects the variable-range hopping conductivity), and the statistics of the charge avalanches induced by a small perturbation of the system. Throughout the talk I will emphasize analogies and differences between electron glasses and spin glasses.