This chapter develops the theory and practice of techniques for improving the efficiency of Monte Carlo integration without necessarily increasing the number of samples. Variance in Monte Carlo ray tracing manifests itself as noise in the image. The battle against variance is the basis of most of the work in optimizing Monte Carlo. Monte Carlo's convergence rate means that it is necessary to quadruple the number of samples in order to reduce the variance by half. Because the run time of the estimation procedure is proportional to the number of samples, the cost of reducing variance can be high. One of the techniques that has been most effective for improving efficiency for rendering problems is a method called importance sampling. Choosing a sampling distribution that is similar in shape to the integrand leads to reduced variance. This technique is called importance sampling because samples tend to be taken in “important” parts of the function's domain, where the function's value is relatively large. The chapter discusses importance sampling and a number of other techniques for improving the efficiency of Monte Carlo. Furthermore the chapter derives techniques for generating samples according to the distributions of BSDFs, light sources, and functions related to volume scattering so that they can be used as sampling distributions for importance sampling.