Time-dependent or immortal bias occurs in data analyses of a time-to-event endpoint where a future exposure status is being treated as known at baseline. Such future exposure can be initial response to treatment, drug exposure, toxicity, or early vs. late start of treatment. Already Anderson et al. (1983) have cautioned that such analyses induce bias. However, empirical investigations still find that these analyses remain persistently common in the clinical literature. In my talk, I will illustrate the issue based on examples and show that, if there is no or a prolonging effect of the time-dependent exposure on the time-to-event, a naive analyses treating the post-baseline exposure as known at baseline will inflate effect estimates. I will discuss features of approaches that are commonly used to address the problem, e.g. landmark analyses or time-varying covariates. The talk will conclude with comments on more advanced methods such as causal inference and joint models, and may highlight connections to the current discussion around estimands.