In survival analysis one is interested in the probability that an event occurs beforeor after certain time points. For example, suppose that for several dental implant systems the probabilities are given that no adverse event occurs during the first five years. This information, possibly complemented by aesthetic or health-conscious aspects, supports the treatment decision and can easily be understood by the patient.Thus often the aim of the statistical analysis is to predict the survival chances ofa tooth, a filling, an implant or a similar study unit. Other important parameters are regression coefficients that describe the influence of patient and tooth specificfactors on the event probabilities, and further measures for the association between event times in the same mouth.Two features complicating the analysis are common for applications of survival analysis to dental research: First, within the framework of a dental study it occurs naturally that the exact event times of some or all study units remain unknown to the data analyst. Besides patient withdrawal, the main reason is that typically the status of the study unit can only be evaluated when the patient is examined by the dentist. Secondly, and this is the most crucial difference to other fields of application, there is often an inherent cluster-correlated structure in the data: two study units placed in the same patient will rarely behave independently.This chapter introduces the statistical concepts and illustrates adaptation of classical survival techniques to applications in dental research. However, due to a lack of methodology and software it will often not be possible to handle all complications at the same time; for example when a regression analysis has to be based on interval censored cluster-correlated event times in the presence of competing risks. We get back to the feasibility issue in the last section.