Summary: Dynamic prediction incorporates time-dependent marker information accrued during follow-up to improve personalized survival prediction probabilities. At any follow-up, or “landmark”, time, the residual time distribution for an individual, conditional on their updated marker values, can be used to produce a dynamic prediction. To satisfy a consistency condition that links dynamic predictions at different time points, the residual time distribution must follow from a prediction function that models the joint distribution of the marker process and time to failure, such as a joint model. To circumvent the assumptions and computational burden associated with a joint model, approximate methods for dynamic prediction have been proposed. One such method is landmarking, which fits a Cox model at a sequence of landmark times, and thus is not a comprehensive probability model of the marker process and the event time. Considering an illness-death model, we derive the residual time distribution and demonstrate that the structure of the Cox model baseline hazard and covariate effects under the landmarking approach do not have simple form. We suggest some extensions of the landmark Cox model that should provide a better approximation. We compare the performance of the landmark models with joint models using simulation studies and cognitive aging data from the PAQUID study. We examine the predicted probabilities produced under both methods using data from a prostate cancer study, where metastatic clinical failure is a time-dependent covariate for predicting death following radiation therapy.