We review the origins, prominent innovations, and major patterns of diversification in suction feeding by vertebrates. Non-vertebrate chordates and larval lamprey suspension-feed by capturing small particles in pharyngeal mucous. In most of these lineages the gentle flows that transport particles are generated by buccal cilia, although larval lamprey and thaliacean urochordates have independently evolved a weak buccal pump to generate an oscillating flow of water that is powered by elastic recovery of the pharynx following compression by buccal muscles. The evolution of jaws and the hyoid facilitated powerful buccal expansion and high-performance suction feeding as found today throughout aquatic vertebrates. We highlight three major innovations in suction feeding. Most vertebrate suction feeders have mechanisms that occlude the corners of the open mouth during feeding. This produces a planar opening that is often nearly circular in shape. Both features contribute to efficient flow of water into the mouth and help direct the flow to the area directly in front of the mouth’s aperture. Among several functions that have been identified for protrusion of the upper jaw, is an increase in the hydrodynamic forces that suction feeders exert on their prey. Protrusion of the upper jaw has evolved five times in ray-finned fishes, including in two of the most successful teleost radiations, cypriniforms and acanthomorphs, and is found in about 60% of living teleost species. Diversification of the mechanisms of suction feeding and of feeding behavior reveals that suction feeders with high capacity for suction rarely approach their prey rapidly, while slender-bodied predators with low capacity for suction show the full range of attack speeds. We hypothesize that a dominant axis of diversification among suction feeders involves a trade-off between the forces that are exerted on prey and the volume of water that is ingested.