Ray-finned fishes make up half of all living vertebrate species. Nearly all ray-finned fishes are teleosts, which include most commercially important fish species, several model organisms for genomics and developmental biology, and the dominant component of marine and freshwater vertebrate faunas. Despite the economic and scientific importance of ray-finned fishes, the lack of a single comprehensive phylogeny with corresponding divergence-time estimates has limited our understanding of the evolution and diversification of this radiation. Our analyses, which use multiple nuclear gene sequences in conjunction with 36 fossil age constraints, result in a well-supported phylogeny of all major ray-finned fish lineages and molecular age estimates that are generally consistent with the fossil record. This phylogeny informs three long-standing problems: specifically identifying elopomorphs (eels and tarpons) as the sister lineage of all other teleosts, providing a unique hypothesis on the radiation of early euteleosts, and offering a promising strategy for resolution of the "bush at the top of the tree" that includes percomorphs and other spiny-finned teleosts. Contrasting our divergence time estimates with studies using a single nuclear gene or whole mitochondrial genomes, we find that the former underestimates ages of the oldest ray-finned fish divergences, but the latter dramatically overestimates ages for derived teleost lineages. Our time-calibrated phylogeny reveals that much of the diversification leading to extant groups of teleosts occurred between the late Mesozoic and early Cenozoic, identifying this period as the "Second Age of Fishes."