Spiny-rayed fishes, or acanthomorphs, comprise nearly one-third of all living vertebrates. Despite their dominant role in aquatic ecosystems, the evolutionary history and tempo of acanthomorph diversification is poorly understood. We investigate the pattern of lineage diversification in acanthomorphs by using a well-resolved time-calibrated phylogeny inferred from a nuclear gene supermatrix that includes 520 acanthomorph species and 37 fossil age constraints. This phylogeny provides resolution for what has been classically referred to as the "bush at the top" of the teleost tree, and indicates acanthomorphs originated in the Early Cretaceous. Paleontological evidence suggests acanthomorphs exhibit a pulse of morphological diversification following the end Cretaceous mass extinction; however, the role of this event on the accumulation of living acanthomorph diversity remains unclear. Lineage diversification rates through time exhibit no shifts associated with the end Cretaceous mass extinction, but there is a global decrease in lineage diversification rates 50 Ma that occurs during a period when morphological disparity among fossil acanthomorphs increases sharply. Analysis of clade-specific shifts in diversification rates reveal that the hyperdiversity of living acanthomorphs is highlighted by several rapidly radiating lineages including tunas, gobies, blennies, snailfishes, and Afro-American cichlids. These lineages with high diversification rates are not associated with a single habitat type, such as coral reefs, indicating there is no single explanation for the success of acanthomorphs, as exceptional bouts of diversification have occurred across a wide array of marine and freshwater habitats.