This chapter deals with models for the analysis of data in which the response variate is the lifetime of a component or the survival time of a patient. Survival data usually refers to medical trials, but the ideas are useful also in industrial reliability experiments where the emphasis is on failure times rather than survival times. Survival data are distinguished from most other types by the widespread occurrence of censoring. Censoring occurs when the outcome of a particular unit (patient or component) is unknown at the end of the study. A distribution for survival times must have a hazard function with suitable properties. The computations can be simplified if the number of distinct covariate vectors is small so that individuals in the risk set may be grouped into sets of constant hazard. The estimation process is less straightforward if the offset contains parameters of the survival density whose values are not known in advance.