We review mechanisms leading to the separation of granular mixtures according to the size or density of the constituent particles. Besides a general overview, the focus of this article is on separation induced by vertical vibrations of the vessel holding the granular material, and specifically on recent results showing a density-dependence to the separation process. A convenient measure of the separation speed is the rise time of a larger “intruder particle” from some fixed initial depth to the free surface, where it will remain. Recent experiments have shown that for large intruder sizes the rise time depends on the density of the intruder particle. Furthermore, in three-dimensional systems we found that this density dependence is highly nonmonotonic. While there is no detailed theoretical understanding available yet, our experiments demonstrate that this surprising behavior is produced by interactions not only between the large intruder particle and the smaller particles of the surrounding granular bed, but also between the particles and the interstitial air.