To ventilate their gills, ray-finned fishes (Actinopterygii) use pumps in their buccal and opercular chambers to alternate between positive and negative pressures, driving water over the gills in a unidirectional current. The basic mechanics are conserved across Actinopterygii, but there is considerable morphological and functional variation of the buccal and opercular pumps. I used comparative approaches to investigate the evolution of ventilatory morphology and function across actinopterygians. In the first chapter, I reconstructed the evolutionary history of restricted gill openings across 433 actinopterygian families using recently published molecular data. Restricted gill openings have evolved at least 11 times among ray-finned fishes with diverse morphology and ecology. Fishes with restricted gill openings also occupied a larger cranial morphospace than fishes with other morphologies. In the second chapter, I studied the gill ventilation of the goosefish, Lophius americanus, which exhibits extremely slow ventilation. I found that the inspiration phase of ventilation is greatly increased relative to that of typical fishes, and that, during this phase, the branchiostegals slowly expand. I described the specialized musculature of the gill opening, which has functional and systematic implications for Lophius. In the third chapter, I studied ventilation function among four sculpins and found considerable variation in buccal and gill chamber pressures. Using phylogenetically corrected generalized least squares models (PGLS), I linked variation in pressures to morphology of the ventilatory pumps, and variation in pressures correlated closely with the size of the branchiostegal 3 apparatus. I propose that adding a third pump to the traditional two-pump model, in which the branchiostegal rays work in parallel with the operculum, is a useful framework for comparative gill ventilatory studies. In the fourth chapter, I reconstructed the phylogeny of sculpins and close relatives (Cottoidei) using published molecular data to analyze measurements of cranial bones from a subset of 23 cottoids. Using PGLS models, I found that suction-feeding associated characters (jaws and operculum) are closely evolutionarily correlated. However, there is only weak correlation between the branchiostegals and these structures. The branchiostegal apparatus may be a source of modularity within gill ventilation that releases constraints imposed by close coupling of feeding and ventilation. 4