AbstractResidual maximum likelihood (REML) is a technique for estimating variance components in multi‐classified data. In contrast to analysis of variance it can be routinely applied to unbalanced data and avoids some of the problems of biased variance estimates found with standard maximum likelihood estimation. The full REML method is of particular value for the analysis of unbalanced clinical trials as it allows recovery of all the available information on treatment effects which can lead to significant improvements in their precision. The use of REML has until recently been limited by heavy computational requirements and lack of readily available software. This is no longer such a restriction, however, as REML procedures are now available in several widely‐used statistical packages, including BMDP, Genstat and SAS. This paper describes the REML technique and discusses its application to three common types of clinical trial: crossover, repeated measures and multicentre.