Replication is the scientific gold standard that enables the confirmation of research findings. Concerns related to publication bias, flexibility in data analysis, and high-profile cases of academic misconduct have led to recent calls for more replication and systematic accumulation of scientific knowledge in psychological science. This renewed emphasis on replication may pose specific challenges to cross-cultural research due to inherent practical difficulties in emulating an original study in other cultural groups. The purpose of the present article is to discuss how the core concepts of this replication debate apply to cross-cultural psychology. Distinct to replications in cross-cultural research are examinations of bias and equivalence in manipulations and procedures, and that targeted research populations may differ in meaningful ways. We identify issues in current psychological research (analytic flexibility, low power) and possible solutions (preregistration, power analysis), and discuss ways to implement best practices in cross-cultural replication attempts.