Over the last three decades, the philosophy of Karl Raimund Popper has had a strong influence on the field of systematic biology. Unequivocally, no other philosopher's work has had such an influence during this formative period in systematics. Much, but not all, of the early discourse on Popper and systematics dealt with the philosophical basis of systematics as a science. More recently Popper's work has been discussed in the systematics literature in relation to specific methodologies such as parsimony and maximum likelihood. In this paper, we provide the reader with a concise summary of Popper's ideas relevant to systematics, review the systematic literature invoking or declining Popper's importance to the field, and make a recommendation for the future course of philosophical thinking in systematics. We try to make clear various authors' interpretations of Popper's work and how those interpretations have impacted systematic thought. Although the reader may come away from this review with a clearer idea of Popper's relevance or lack thereof, our primary hope is that the reader will be compelled to question him- or herself about the philosophical basis of the systematic work that he or she does, and to delve into the literature herein cited. We begin by presenting a synopsis of Popper's philosophical views to allow those views to be placed in the context of systematics.