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Fish in nature have several distinct advantages over traditional propeller driven underwater vehicles including maneuverability and flow sensing capabilities. Taking inspiration from biology, this work seeks to answer three questions related to bioinspired pursuit and apply the knowledge gained therein to the control of a novel, reaction-wheel driven autonomous fish robot. Which factors are most important to a successful pursuit? How might we guarantee capture with underwater pursuit? How might we track the wake of a flapping fish or vehicle? A technique called probabilistic analytical modeling (PAM) is developed and illustrated by the interactions between predator and prey fish in two case studies that draw on recent experiments. The technique provides a method for investigators to analyze kinematics time series of pursuit to determine which parameters (e.g. speed, flush distance, and escape angles) have the greatest impact on metrics such as probability of survival. Providing theoretical guarantees of capture become complicated in the case of a swimming fish or bioinspired fish robot because of the oscillatory nature fish motion. A feedback control law is shown to result in forward swimming motion in a desired direction. Analysis of this law in a pursuit scenario yields a condition stating whether capture is guaranteed provided some basic information about the motion of the prey. To address wake tracking inspiration is taken from the lateral line sensing organ in fish, which is sensitive to hydrodynamic forces in the local flow field. In experiment, an array of pressure sensors on a Joukowski foil estimates and controls flow-relative position in a Karman vortex street using potential flow theory, recursive Bayesian filtering, and trajectory-tracking, feedback control. The work in this dissertation pushes the state of the art in bioinspired underwater vehicles closer to what can be found in nature. A modeling technique provides a means to determine what is most imp