In many natural materials, such as skin, minerals, and plastics, light scatters inside the material and gives them their distinctive appearance. The accurate reproduction of these materials requires new rendering algorithms that can simulate these subsurface interactions. Unfortunately, adding subsurface scattering dramatically increases the rendering cost. To achieve efficiency, recent approaches have used an approximate scattering model and have two signifficant limitations: they scale poorly to complex scenes and they are limited to homogeneous materials. This thesis proposes two new algorithms without these limitations. The ffirst is a scalable, subsurface renderer for homogeneous scattering. Using a canonical model of subsurface light paths, the new algorithm can judiciously determine a small set of important paths. By clustering the unimportant paths and approximating the contributions of these clusters, the new algorithm signifficantly reduces computation. In complex scenes, this new approach can achieve up to a three hundred fold speedup over the most efficient previous algorithms. The second is the ffirst, general, efficient and high-quality renderer for heterogeneous subsurface scattering. It based on a carefully derived formulation of the heterogeneous scattering problem using the diffusion equation and it solves that problem quickly and accurately using the finite element method. The new algorithm is designed for high-quality rendering applications producing, in minutes, images nearly identical to exact solutions produced in hours.