Longevity records have two unique features requiring special statistical tools: first, part of the data is often censored: only a lower bound of the true longevity is known, e.g., when the animals are still alive. Under certain assumptions, it is possible to define the correct likelihood contribution of such records. Then, standard likelihood methodology can be applied. Second, explanatory variables are often time‑dependent (their value changes with time). The concept of hazard function, defined as the limiting rate of death at time t, conditional upon survival to time t, allows a natural modeling of the relationship between longevity and these covariates. In proportional hazards models, the hazard function of an animal is described as the product of a baseline function and an exponential function of the covariates. This formulation allows an intuitive interpretation of the effect of each covariate in terms of relative risk of dying. Extensions to mixed models, e.g., with inclusion of genetic effects have been proposed, as well as methods for the estimation of the corresponding variance components. After a long presentation of the background, two examples are presented to illustrate the features and potential uses of survival analysis: a genetic evaluation of bulls based on the longevity of their daughters and an analysis of the effect of disease occurrence on culling.