This thesis deals with frailty modelling, a framework devised to analyse clustered survival data. The main focus is on modelling the frailty term. The frailty term captures the dependence of survival times within a cluster and the heterogeneity between clusters. Typical is that the frailty term is treated as a random effect. Different distributions have been proposed to model the frailty term. Contributions of this thesis include a unified framework for fitting the frailty model with different frailty distributions, a new diagnostic plot to evaluate the frailty distribution assumption, a simulation study to assess robustness of regression inference against frailty misspecification, and a method to test for decreasing cluster heterogeneity in a new time-varying frailty model. Also presented is a first step towards modelling spatial dependence in survival data by means of spatially correlated frailties.