Due to the advances in medical research in the past decades, cancer is not necessarily a fatal disease anymore. For specific cancer types, one can now reasonably expect a fraction of long-term survivors to show-up in cancer clinical trials. The presence of short-and long-term survivors may lead to a violation of the proportional hazards assumption and therefore jeopardize the use of of the popular Cox model. Furthermore, in such a situation, the proportion of “cured” patients becomes a crucial component of the assessment of patient benefit, and being able to distinguish a curative from a life-prolonging effect conveys important additional information in the evaluation of a new treatment. To address these issues, specific “cure models” have been proposed in the statistical literature. In this chapter we introduce the two main families of such models: mixture cure models and promotion time cure models. We elaborate on how and when to use these models and discuss that in practice, it is not only a matter of whether or not there are cured patients in the data, but that as in classical survival analysis, the appropriate model to be used should be carefully chosen, based on the main features of the data and with a strong emphasis on the proportional hazards assumption.