The present issue of "JRME" features three articles--Melhuish (2018; see EJ1167195); Jamil, Larsen, and Hamres (2018; see EJ1167178); and Thanheiser (2018; see EJ1167179)--that involve, at least to some degree, replication of prior published studies. In each of these articles, the authors provide a clear rationale for the importance of the work, and in all three cases, the importance of replication of prior work is discussed. The authors of these three articles point out that the scientific community writ large values replication, and they also note that replication is quite rare in educational research generally and in mathematics education research more specifically. In this commentary, the author directly addresses the issue of replication of research in the field of mathematics education and seeks to provide guidance to journals in mathematics education (and thus indirectly to authors of articles submitted to journals) on when and why replication studies should be published. The author identifies three criteria for evaluating the quality of articles describing replication studies that be used to determine whether a replication study merits publication in a top-tier journal.