Boxfishes (family Ostraciidae) are tropical reef-dwelling marine bony fishes that have about three-fourths of their body length encased in a rigid bony test. As a result, almost all of their swimming movements derive from complex combinations of movements of their median and paired fins (MPF locomotion). In terms of both body design and swimming performance, they are among the most sophisticated examples known of naturally evolved vertebrate autonomous underwater vehicles. Quantitative studies of swimming performance, biomechanics, and energetics in one model species have shown that (i) they are surprisingly strong, fast swimmers with great endurance; (ii) classical descriptions of how they swim were incomplete: they swim at different speeds using three different gaits; (iii) they are unusually dynamically well controlled and stable during sustained and prolonged rectilinear swimming; and (iv) despite unusually high parasite (fuselage) drag, they show energetic costs of transport indistinguishable from those of much better streamlined fishes using body and caudal fin (BCF) swimming modes at similar water temperatures and over comparable ranges of swimming speeds. We summarize an analysis of these properties based on a dynamic model of swimming in these fishes. This model accounts for their control, stability, and efficiency in moving through the water at moderate speeds in terms of gait changes, of water-flow patterns over body surfaces, and of complex interactions of thrust vectors generated by fin movements.