Many of the dependent variables analyzed in the social sciences involve a time period of nonoccurrence prior to their occurrence. Demographers study death; but one cannot die without being born. Thus, one’s death is preceded by a time period after the person has been born during which time they do not die. Such a dependent variable is referred to as a time-to-event variable because there must be a time period of nonoccurrence before the event occurs. Such analyses have several names. The broadest ones are survival analysis or hazard analysis, owing to their early development in biostatistics and epidemiology, where researchers modeled the occurrence of death. The event of death was referred to as a hazard. Persons over a time interval not experiencing the hazard, that is, not dying, were referred to as surviving the hazard. There are two main types of survival models, continuous-time models and discrete-time methods. We direct most of our attention in this chapter to continuous-time models of survival analysis, and specifically to the Cox proportional hazard model. In the last section of the chapter, we focus on discrete-time survival models.