Time-varying covariates present special problems in survival analyses. Their measurements are often missing, and their missing status may be related to the survival outcome of interest. This dissertation discusses three approaches to handling time-varying covariates in survival models. First, predictions of event probabilities from a joint model for longitudinal and event time data are are compared to predictions from simpler models. Second, a Bayesian joint modeling approach is used to resolve difficulties relating to inference when measurements of a potentially mediating process are partially missing. Third, many time-varying covariates can be converted into alternative time scales. This dissertation presents an approach to handle vector-valued time scales in semiparametric proportional hazards regression.