One of the simplest and most common techniques for dealing with the aliasing of shadow edges is called percentage-closer filtering (PCF). The name comes from the concept of sampling the area around the fragment and determining the percentage of the area that is closer to the light source (in shadow). The percentage is then used to scale the amount of (diffuse and specular) shading that the fragment receives. The overall effect is a blurring of the shadow's edges.
The basic technique was first published by Reeves et al in a 1987 paper (SIGGRAPH Proceedings, Volume 21, Number 4, July 1987). The concept involved transforming the fragment's extents into shadow space, sampling several locations within that region, and computing the percent that is closer than the depth of the fragment. The result is then used to attenuate the shading. If the size of this filter region is increased, it can have the effect of blurring the shadow's edges.