Fishes are both extremely diverse and morphologically disparate. Part of this disparity can be observed in the numerous possible fin configurations that may differ in terms of the number of fins as well as fin shapes, sizes and relative positions on the body. Here, we thoroughly review the major patterns of disparity in fin configurations for each major group of fishes and discuss how median and paired fin homologies have been interpreted over time. When taking into account the entire span of fish diversity, including both extant and fossil taxa, the disparity in fin morphologies greatly complicates inferring homologies for individual fins. Given the phylogenetic scope of this review, structural and topological criteria appear to be the most useful indicators of fin identity. We further suggest that it may be advantageous to consider some of these fin homologies as nested within the larger framework of homologous fin‐forming morphogenetic fields. We also discuss scenarios of appendage evolution and suggest that modularity may have played a key role in appendage disparification. Fin modules re‐expressed within the boundaries of fin‐forming fields could explain how some fins may have evolved numerous times independently in separate lineages (e.g., adipose fin), or how new fins may have evolved over time (e.g., anterior and posterior dorsal fins, pectoral and pelvic fins). We favour an evolutionary scenario whereby median appendages appeared from a unique field of competence first positioned throughout the dorsal and ventral midlines, which was then redeployed laterally leading to paired appendages.