Empirical likelihood (EL) is a recently developed nonparametric method of statistical inference. Owen’s 2001 book contains many important results for EL with uncensored data. However, fewer results are available for EL with right-censored data. In this dissertation, we first investigate a right-censored-data extension of Qin and Lawless (1994). They studied EL with uncensored data when the number of estimating equations is larger than the number of parameters (over-determined case). We obtain results similar to theirs for the maximum EL estimator and the EL ratio test, for the over-determined case, with right-censored data. We employ hazard-type constraints which are better able to handle right-censored data. Then we investigate EL with right-censored data and a k-sample mixed hazard-type constraint. We show that the EL ratio test statistic has a limiting chi-square distribution when k = 2. We also study the relationship between the constrained Kaplan-Meier estimator and the corresponding Nelson-Aalen estimator. We try to prove that they are asymptotically equivalent under certain conditions. Finally we present simulation studies and examples showing how to apply our theory and methodology with real data.