Baleen whales are obligate filter feeders, straining prey‐laden seawater through racks of keratinized baleen plates. Despite the importance of baleen to the ecology and natural history of these animals, relatively little work has been done on baleen morphology, particularly with regard to the three‐dimensional morphology and structure of baleen. We used computed tomography (CT) scanning to take 3D images of six baleen specimens representing five species, including three complete racks. With these images, we described the three‐dimensional shape of the baleen plates using cross‐sectional profiles from within the gum tissue to the tip of the plates. We also measured the percentage of each specimen that was composed of either keratinized plate material or was void space between baleen plates, and thus available for seawater flow. Baleen plates have a complex three‐dimensional structure with curvature that varies across the anterior‐posterior, proximal‐distal, and medial‐lateral (lingual‐labial) axes. These curvatures also vary with location along the baleen rack, and between species. Cross‐sectional profiles resemble backwards‐facing airfoils, and some specimens display S‐shaped, or reflexed, camber. Within a baleen specimen, the intra‐baleen void volume correlates with the average bristle diameter for a species, suggesting that essentially, thinner plates (with more space between them for flow) have thinner bristles. Both plate curvature and the relative proportions of plate and void volumes are likely to have implications for the mechanics of mysticete filtration, and future studies are needed to determine the particular functions of these morphological characters. Anat Rec, 300:1942–1952, 2017. © 2017 The Authors The Anatomical Record published by Wiley Periodicals, Inc. on behalf of American Association of Anatomists