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In this talk, we explore the modeling of survival data in the presence of longitudinal covariates. In particular, we consider survival data that are subject to both left truncation and right censoring. It is well known that traditional approaches, such as the partial likelihood approach for the Cox proportional hazards model encounter difficulties when longitudinal covariates are involved in the modeling of the survival data. A joint likelihood approach has been shown in the literature to provide an effective way to overcome those difficulties for right censored data. However, in the presence of left truncation, there are additional challenges for the joint likelihood approach. We propose an alternative likelihood to overcome these difficulties and establish the asymptotic theory, including semiparametric efficiency of the new approach. The approach will also be illustrated numerically. *The talk is based on joint work with Yu-Ru Su, National Cheng-Kun University, Taiwan.