This paper reviews nonparametric methods for the analysis of crossover studies. Primary attention is given to crossover studies to compare two treatments for a response variable that has a metric measurement level. For this situation, one can often test hypotheses or obtain confidence intervals for parameters of interest by applying well known univariate nonparametric rank methods (e.g., the Wilcoxon rank sum test, or the Wilcoxon signed rank test) to appropriately specified functions of the data. Related extensions are also available, to some degree, for crossover studies to compare more than two treatments or those for which the measurement level of the response variable is ordinal or has a censored time-to-event nature. Methods for several specific situations along these lines are discussed in terms of principles with potentially broader applicability. Several examples are provided to illustrate the performance of some of the methods.