Replication has long been a cornerstone for establishing trustworthy scientific results, but there remains considerable disagreement about what constitutes a replication, how results from these studies should be interpreted, and whether direct replication of results is even possible. This article addresses these concerns by presenting the methodological foundations for a replication science. It provides an introduction to the causal replication framework, which defines “replication” as a research design that tests whether two (or more) studies produce the same causal effect within the limits of sampling error. The framework formalizes the conditions under which replication success can be expected, and allows for the causal interpretation of replication failures. Through two applied examples, the article demonstrates how the causal replication framework may be utilized to plan prospective replication designs, as well as to interpret results from existing replication efforts.