Despite widespread interest in the development of process-based psychotherapies, little is still known about the underlying processes that underpin our most effective therapies. Statistical mediation analysis is a commonly used analytical method to evaluate how, or by which processes, a therapy causes change in an outcome. Causal mediation analysis (CMA) represents a new advancement in mediation analysis that employs causally-defined direct and indirect effects based on potential outcomes. These novel ideas and analytical techniques have been characterized as revolutionary in epidemiology and biostatistics, although they are not (yet) widely known among researchers in clinical psychology. In this paper, I outline the fundamental concepts underlying CMA, clarify the differences between the CMA approach and the traditional approach to mediation, and identify two important data analytical aspects that have been emphasized as a result of these recent advancements. To illustrate the key ideas, assumptions, and mathematical definitions intuitively, an applied clinical example from a previously published randomized controlled trial is used. CMA's main contributions are discussed, as well as some of the key challenges. Finally, it is argued that the most significant contribution of CMA is the formalization of mediation in a unified causal framework with clear assumptions.