Teeth are often the first structures that anatomists and paleontologists examine to understand the ecology and morphology of feeding, both because teeth are highly specialized structures that provide precise information, and because they are among the best and most commonly preserved fossils. Unfortunately, many fragmentary fossil and recent specimens lack teeth, and some come from edentulous individuals and taxa, as in mysticete (baleen) whales. In our broad comparative review, we survey non-dental osteological features that, due to size, shape, arrangement, and surface features reflecting muscle attachments, provide useful clues to general or specific aspects of prey capture, intraoral transport, processing, or swallowing. We focus on hyoid, palatal, and pterygoid bones, mandibular symphyses and processes such as the coronoid, and the temporal fossa and zygomatic arch, as well as adjacent cranial bones relating to oral and pharyngeal anatomy. These bones relate to muscles of five general locations especially indicative of feeding: mandibular, hyoid, tongue, pharyngeal, and facial regions. Together these bones and muscles affect feeding and related activities including suckling and breathing. We discuss osteological correlates that provide special relevance to key transitions in cetacean evolutionary history, such as the shift from predominantly terrestrial to aquatic feeding, the shift from typical mammalian mastication to swallowing prey entirely or nearly whole, and the separation of respiratory and digestive passages. We also point to examples of modern specialists in these anatomical optima for different modes of prey capture, intraoral transport, processing, and swallowing. Although we focus on cetaceans, our approach is broadly relevant to all vertebrates, notably other marine tetrapods.