The Cox model is one of the most widely used semi-parametric models in survival data analysis. For various types of censored data, such as left truncated and right censored data, doubly censored data, bivariate right censored data, bivariate data under univariate censoring, etc., the studies of statistical inferences on the Cox model become very difficultand challenging. Until now little work has been done for the Cox model with these complicated types of censored data. Among existing works, most of them are not likelihood-based and are case-by-case methods, which are not directly applicable to other types of censored data. In this dissertation, we extend the concept of weighted empirical likelihood (Ren, 2001, 2008) from univariate case to multivariate case, then we develop an estimation method for the Cox model that is applicable to various types of censored data under a unified framework. A computing algorithm for our proposed procedure is developed and some simulation results are presented.