Precedence tests are simple yet robust nonparametric procedures useful for comparing two or more distributions. In this paper precedence type tests are considered when the data contain some right-censored observations. Generalizing the precedence statistic for uncensored data, the precedence tests for censored data are based on the Kaplan-Meier estimators of the respective distribution functions and the corresponding quantile functions. An overview of the literature is given for the two-sample as well as some multi-sample problems. Some further problems are indicated.