Significance Nature provides diverse solutions to passive visual depth sensing. Evolution has produced vision systems that are highly specialized and efficient, delivering depth-perception capabilities that often surpass those of existing artificial depth sensors. Here, we learn from the eyes of jumping spiders and demonstrate a metalens depth sensor that shares the compactness and high computational efficiency of its biological counterpart. Our device combines multifunctional metalenses, ultrathin nanophotonic components that control light at a subwavelength scale, and efficient computations to measure depth from image defocus. Compared with previous passive artificial depth sensors, our bioinspired design is lightweight, single-shot, and requires a small amount of computation. The integration of nanophotonics and efficient computation establishes a paradigm for design in computational sensing.