The opportunities presented by swimming have considerably shaped the evolution of life on our planet. All life, extinct and extant, must abide by the same physical laws. Through an understanding of these physical properties, we can place quantitative constraints on the life habits and ecological roles of extinct organisms. Open-source tools and other emerging technologies can help answer broad questions in paleobiology by enabling detailed reconstructions of fossils and the biomechanical properties of their once-living counterparts. This talk will focus on using such an approach (involving computer modeling, robotics, and other tools) to investigate the aquatic biomechanics of a model system spanning ~0.5 billion years – the externally shelled cephalopods (i.e., ammonoids and nautiloids). The evolutionary history of these animals, and their hydromechanical properties, illuminate unique solutions to the obstacles presented by aquatic locomotion, involving buoyancy, stability, maneuverability, control, and locomotive efficiency. These form-function relationships add context to early benthic-nektic transitions and various marine radiations, while highlighting fundamental constraints on aquatic locomotion more broadly.