Mechanosensation is a universal feature of animals that is essential for behavior, allowing detection of animals' own body movement and position as well as physical characteristics of the environment. The extraordinary morphological and behavioral diversity that exists across fish species provide rich opportunities for comparative mechanosensory studies in fins. The fins of fishes have been found to function as proprioceptors, by providing feedback on fin ray position and movement, and as tactile sensors, by encoding pressures applied to the fin surface. Across fish species, and among fins, the afferent response is remarkably consistent, suggesting that the ability of fin rays and membrane to sense deformation is a fundamental feature of fish fins. While fin mechanosensation has been known in select, often highly specialized, species for decades, only in the last decade have we explored mechanosensation in typical propulsive fins and considered its role in behavior, particularly locomotion. In this paper, we synthesize the current understanding of the anatomy and physiology of fin mechanosensation, looking toward key directions for research. We argue that a mechanosensory perspective informs studies of fin-based propulsion and other fin-driven behaviors and should be considered in the interpretation of fin morphology and behavior. In addition, we compare the mechanosensory system innervating the fins of fishes to the systems innervating the limbs of mammals and wings of insects in order to identify shared mechanosensory strategies and how different organisms have evolved to meet similar functional challenges. Finally, we discuss how understanding the biological organization and function of fin sensors can inform the design of control systems for engineered fins and fin-driven robotics.