In the context of randomized intervention trials, we describe causal methods for analyzing how post-randomization factors constitute the process through which randomized baseline interventions act on outcomes. Traditionally, such mediation analyses have been undertaken with great caution, because they assume that the mediating factor is also randomly assigned to individuals in addition to the randomized baseline intervention (i.e., sequential ignorability). Because the mediating factors are typically not randomized, such analyses are unprotected from unmeasured confounders that may lead to biased inference. We review several causal approaches that attempt to reduce such bias without assuming that the mediating factor is randomized. However, these causal approaches require certain interaction assumptions that may be assessed if there is enough treatment heterogeneity with respect to the mediator. We describe available estimation procedures in the context of several examples from the literature and provide resources for software code.