Multivariate failure time data are important in biomedical research. While statistical methods for univariate failure time data are well established, the corresponding standard analysis tools for multivariate failure time data have not yet been established. The main difficulty is that with multiple censored time-to-disease outcomes, the joint likelihood is non-uniquely due to uninformative data points concerning the local dependency between event times. This talk will focus on some recent development in this area, including nonparametric estimates of joint survival function, average dependency measure, and semiparametric regression models of the cross ratio process. The proposed methods has the ability to explore and estimate dependency between event times as well as to understand the relationship between dependency and risk factors. Simulation evaluations as well as an application to the Women's Health Initiative's hormone therapy trial will be presented.