The AB/BA design is reviewed from a historical perspective. Particular attention is paid to the problem of carry-over and various attempts to deal with it. The two-stage procedure, an approach which was popular for many years, is shown to be unsafe. The analysis of AB/BA designs with baseline data is also considered. It is shown that such baselines do not provide a cure for the problem of carry-over; and it is concluded that any rational analysis of such trials will always be dependent on assumptions regarding carry-over, and that it is necessary to pay particular attention to washout periods. Under such circumstances analysis of covariance may be useful. In conclusion, some speculative comments about future lines of research are offered.