Replication is complicated in psychological research because studies of a given psychological phenomenon can never be direct or exact replications of one another, and thus effect sizes vary from one study of the phenomenon to the next-an issue of clear importance for replication. Current large-scale replication projects represent an important step forward for assessing replicability, but provide only limited information because they have thus far been designed in a manner such that heterogeneity either cannot be assessed or is intended to be eliminated. Consequently, the nontrivial degree of heterogeneity found in these projects represents a lower bound on the true degree of heterogeneity. We recommend enriching large-scale replication projects going forward by embracing heterogeneity. We argue this is the key for assessing replicability: if effect sizes are sufficiently heterogeneous-even if the sign of the effect is consistent-the phenomenon in question does not seem particularly replicable and the theory underlying it seems poorly constructed and in need of enrichment. Uncovering why and revising theory in light of it will lead to improved theory that explains heterogeneity and increases replicability. Given this, large-scale replication projects can play an important role not only in assessing replicability but also in advancing theory.