Trials of new oncology treatments often involve a crossover element in their design that allows patients receiving the control treatment to crossover to receive the experimental treatment at disease progression or when sufficient evidence about the efficacy of the new treatment is achieved. Crossover leads to contamination of the initial randomized groups due to a mixing of the effects of the control and experimental treatments in the reference group. This is further complicated by the fact that crossover is often a very selective process whereby patients who switch treatment have a different prognosis than those who do not. Standard statistical techniques, including those that attempt to account for the treatment switch, cannot fully adjust for the bias introduced by crossover. Specialized methods such as rank-preserving structural failure time (RPSFT) models and inverse probability of censoring weighted (IPCW) analyses are designed to deal with selective treatment switching and have been increasingly applied to adjust for crossover. We provide an overview of the crossover problem and highlight circumstances under which it is likely to cause bias. We then describe the RPSFT and IPCW methods and explain how these methods adjust for the bias, highlighting the assumptions invoked in the process. Our aim is to facilitate understanding of these complex methods using a case study to support explanations. We also discuss the implications of crossover adjustment on cost-effectiveness results.