Crossover designs are useful and popular for certain experiments in a variety of fields, including in the pharmaceutical industry. In some applications they enjoy important advantages over parallel trials, but they also induce a number of potential problems not faced with parallel trials. The possible presence of carryover effects is one of these. Partly as a result of this, a number of different models have been considered for analyzing data from a crossover design. In this talk we will focus on the optimal design question. Thus, given that we want to use a certain model, what is a good design to use? We will restrict our attention to the situation that only two treatments are to be compared in the experiment.