Classification of the tremendous diversity of ray-finned fishes (Actinopterygii) began with the designation of taxonomic groups based on morphological similarity. Starting in the late 1960s morphological phylogenetics became the basis for the classification of Actinopterygii but failed to resolve many relationships, particularly among lineages within the hyperdiverse Percomorpha. The introduction of molecular phylogenetics led to a dramatic reconfiguration of actinopterygian phylogeny. Refined phylogenetic resolution afforded by molecular studies revealed an uneven diversity among actinopterygian lineages, resulting in a proliferation of redundant group names in Linnean ranked classifications. Here we provide an unranked phylogenetic classification for actinopterygian fishes based on a summary phylogeny of 830 lineages of ray-finned fishes that includes all currently recognized actinopterygian taxonomic families and 287 fossil taxa. We provide phylogenetic definitions for 90 clade names and review seven previously defined names. For each of the 97 clade names we review the etymology of the clade name, clade species diversity and constituent lineages, clade diagnostic morphological apomorphies, a review of synonyms, and discuss the clade's nomenclatural and systematic history. The new classification is free of redundant group names and includes only one new name among the 97 clade names we review and describe, yielding a comprehensive classification that is based explicitly on the phylogeny of ray-finned fishes that has emerged in the 21st century and rests on the foundation of the previous 200 years of actinopterygian systematic research.