Arthur Cropley (2006) emphasized the critical place that convergent thinking has in creativity. Although he briefly refers to the blind variation and selective retention (BVSR) theory of creativity, his discussion could not reflect the most recent theoretical and empirical developments in BVSR, especially the resulting combinatorial models. Therefore, in this article I first provide an overview of contemporary BVSR theory, including both a general combinatorial model and its specific manifestations (internal vs. external selection, simultaneous vs. sequential selection, exploration vs. elimination, and open vs. closed preselection). This overview then permits theoretical treatment of the connections between convergent thinking and BVSR. These connections entail the direct involvement of convergent thinking in BVSR, as well as the occasions in which sequential BVSR operates in a manner resembling convergent thinking. The article closes with a discussion of some misunderstandings regarding the function of domain-specific knowledge in BVSR creativity. This discussion includes the argument that hindsight bias often makes creativity appear far more knowledge based than it was at the time the creative ideas first emerged. This bias can make researchers overlook how BVSR mediates between expertise and creativity. Hence, care must be taken not to bypass BVSR in granting all due credit to convergent thinking.