This chapter describes crossover trials and their applications in neurology. Crossover trials could be used to study aspects of many common neurological disorders and psychiatric disorders. To illustrate the efficiency of crossover designs, the chapter presents sample size estimates for two placebo-controlled parallel and one crossover design for a trial examining the efficiency of donepezil in treating dementia in patients with Parkinson's disease. It also describes approaches to mitigate carryover effects. Alternatives to the 2 x 2 design are used to increase efficiency, provide unbiased estimates in the presence of carryover effects, and to compare more than two treatments. This chapter reviews response adaptive designs, matching and N of 1 trial along with several recent innovations in design. Simple carryover depends only on the treatment in the period prior to when carryover occurs. Crossover trials have logistical challenges beyond the careful planning and implementation that accompanies any successful clinical trial.