We review recent developments in size separation in vibrated granular materials. Motivated by a need in industry to handle granular materials efficiently and a desire to make fundamental advances in non-equilibrium physics, experimental and theoretical investigations have shown size separation to be a complex phenomenon. Large particles in a vibrated granular system normally rise to the top. However, they may also sink to the bottom or show other patterns, depending on subtle variations in physical conditions. While size ratio is a dominant factor, particle-specific properties such as density, inelasticity and friction can play an important role. The nature of the energy input, boundary conditions and interstitial air have also been shown to be significant factors in determining spatial distributions. The presence of convection can enhance mixing or lead to size separation. Experimental techniques including direct visualization and magnetic resonance imaging are being used to investigate these properties. Molecular dynamics and Monte Carlo simulation techniques have been developed to probe size separation. Analytical methods such as kinetic theory are being used to study the interplay between particle size and density in the vibro-fluidized regime, and geometric models have been proposed to describe size separation for deep beds. Besides discussing these studies, we will also review the impact of inelastic collisions and friction on the density and velocity distributions to gain a deeper appreciation of the non-equilibrium nature of the system. While a substantial number of studies have been performed, considerable work is still required to achieve a firm description of the phenomena.