Many biomedical studies follow participants for multiple correlated health outcomes. Modeling these outcomes simultaneously opens the possibility of understanding an individual’s susceptibility to multiple diseases through the life span. 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-event 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 a nonparametric and a semiparametric approach of estimating the joint survival function. These proposed methods have 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.