This chapter discusses censored time-to-event data. We review and define right-censored and interval-censored data and common assumptions associated with them, focusing on standard cases when the independent censoring assumption holds. We define the Kaplan–Meier estimator, the nonparametric maximum likelihood estimator (NPMLE) for the survival distribution for right censored data. We describe the beta product confidence procedure which gives pointwise confidence intervals for it, with better coverage than the standard Greenwood intervals. We describe the NPMLE for the survival distribution for interval censored data using the E-M algorithm. We compare the proportional hazards or proportional odds models. For both right- and interval-censored data, we describe the score tests from the proportional hazards or odds models, and show they are different forms of weighted logrank tests. We cover testing the difference in survival distributions at a specific point in time. We discuss issues with interpreting the proportional hazards model causally, showing that a model with individual proportional hazards does not equal the usual population proportional hazards model.