Researchers have long accepted that statistical conclusion validity, internal validity, construct validity, and external validity are all critical considerations in the conduct and evaluation of psychological research. A thorough understanding of the relevant issues should help to highlight likely relations among the causes of failures to replicate. This chapter shows that validities approach can help to identify those relations as well as the trade-offs that should be considered in designing and interpreting replication research. Perhaps the most explicit discussion of construct validity to date has revolved around the issue of psychometric invariance, but construct validity has also appeared in discussions of so-called exact versus conceptual replication. The validities approach can also assist in understanding and predicting when and why failures to replicate are likely to occur. Such understanding should also suggest strategies for designing replication studies and follow-up research when replication studies fail to produce the expected results.