Nonparametric estimation of a conditional mean function in regression has received a lot of attention. Apart from the mean function, also estimation of the conditional variance function (the error variance) is of interest. This paper reviews the main approaches in estimation of the error variance in regression: difference-based and residual-based procedures. Which specific statistical methods are appropriate very much depends on whether the design is fixed or random, and the regression context is homoscedastic or heteroscedastic. We present the review keeping these issues in mind, and discuss some recent contributions in error variance estimation. For simplicity of presentation we restrict to kernel methods in this paper.