Survival analysis is one of the core research methods used in many fields such as medicine, biology, epidemiology, demography, and engineering. Notion survival analysis reflects the origin of the methods in medical and demographic studies of mortality. Especially since the end of the 1970s, the empirical analysis of event history data has become widespread by the development of the proportional hazards model in the seminal paper by Cox (1972) and several extensions during the last three decades. The present monograph deals with one important direction of extensions in this field, namely frailty models. A frailty model is a multiplicative hazard model consisting of three components: a frailty (random effect), a baseline hazard function (parametric or nonparametric), and a term modeling the influence of observed covariates (fixed effects).