Stepped wedge designs (SWDs) have received considerable attention recently, as they are potentially a useful way to assess new treatments in areas such as health services implementation. Because allocation is usually by cluster, SWDs are often viewed as a form of cluster‐randomized trial. However, since the treatment within a cluster changes during the course of the study, they can also be viewed as a form of crossover design. This article explores SWDs from the perspective of crossover trials and designed experiments more generally. We show that the treatment effect estimator in a linear mixed effects model can be decomposed into a weighted mean of the estimators obtained from (1) regarding an SWD as a conventional row‐column design and (2) a so‐called vertical analysis, which is a row‐column design with row effects omitted. This provides a precise representation of “horizontal” and “vertical” comparisons, respectively, which to date have appeared without formal description in the literature. This decomposition displays a sometimes surprising way the analysis corrects for the partial confounding between time and treatment effects. The approach also permits the quantification of the loss of efficiency caused by mis‐specifying the correlation parameter in the mixed‐effects model. Optimal extensions of the vertical analysis are obtained, and these are shown to be highly inefficient for values of the within‐cluster dependence that are likely to be encountered in practice. Some recently described extensions to the classic SWD incorporating multiple treatments are also compared using the experimental design framework.