BackgroundFishes are extremely speciose and also highly disparate in their fin configurations, more specifically in the number of fins present as well as their structure, shape, and size. How they achieved this remarkable disparity is difficult to explain in the absence of any comprehensive overview of the evolutionary history of fish appendages. Fin modularity could provide an explanation for both the observed disparity in fin configurations and the sequential appearance of new fins. Modularity is considered as an important prerequisite for the evolvability of living systems, enabling individual modules to be optimized without interfering with others. Similarities in developmental patterns between some of the fins already suggest that they form developmental modules during ontogeny. At a macroevolutionary scale, these developmental modules could act as evolutionary units of change and contribute to the disparity in fin configurations. This study addresses fin disparity in a phylogenetic perspective, while focusing on the presence/absence and number of each of the median and paired fins.ResultsPatterns of fin morphological disparity were assessed by mapping fin characters on a new phylogenetic supertree of fish orders. Among agnathans, disparity in fin configurations results from the sequential appearance of novel fins forming various combinations. Both median and paired fins would have appeared first as elongated ribbon-like structures, which were the precursors for more constricted appendages. Among chondrichthyans, disparity in fin configurations relates mostly to median fin losses. Among actinopterygians, fin disparity involves fin losses, the addition of novel fins (e.g., the adipose fin), and coordinated duplications of the dorsal and anal fins. Furthermore, some pairs of fins, notably the dorsal/anal and pectoral/pelvic fins, show non-independence in their character distribution, supporting expectations based on developmental and morphological evidence that these fin pairs form evolutionary modules.ConclusionsOur results suggest that the pectoral/pelvic fins and the dorsal/anal fins form two distinct evolutionary modules, and that the latter is nested within a more inclusive median fins module. Because the modularity hypotheses that we are testing are also supported by developmental and variational data, this constitutes a striking example linking developmental, variational, and evolutionary modules.Electronic supplementary materialThe online version of this article (doi:10.1186/s12915-017-0370-x) contains supplementary material, which is available to authorized users.