Causal mediation analysis is considered for time-to-event outcomes and survival analysis models. Different possible effect decompositions are discussed for the survival function, hazard, mean survival time and median survival scales. Approaches to mediation analysis in the social sciences are related to counterfactual approaches using additive hazard, proportional hazard and accelerated failure time models. The product-coefficient method from the social sciences gives mediated effects on the hazard difference scale for additive hazard models, on the log mean survival time difference scale for accelerated failure time models, and on the log hazard scale for the proportional hazards model but only if the outcome is rare. With the proportional hazards model and a common outcome, the product-coefficient method can provide a valid test for the presence of a mediator effect but does not provide a measure. When additive hazard, accelerated failure time, or the rare-outcome proportional hazards models are employed and combined with the counterfactual approach, exposure-mediator interactions can be accommodated in a relatively straightforward manner.