This paper reviews the studies on the kinematics, hydrodynamics, and performance of median and paired fin (MPF) in fish and biomimetic mechanical systems from the viewpoint of enhancing the propulsive and maneuvering performance of marine vehicles at low speeds. Precise maneuverability and stability at low swimming speeds by use of MPF propulsion seem to be advantageous in complex habitats such as coral reefs. MPF propulsion in fish consists of undulatory fin motion and oscillatory fin motion. The kinematics of MPF in fish and mechanical systems in both groups is discussed. Hydrodynamic models and experimental data of undulatory and oscillatory motions of MPF in fish and mechanical system are reviewed. Pectoral fin propulsion has two categories which represent biomechanical extremes in the use of appendages for propulsion: drag-based and lift-based mechanisms of thrust production. The hydrodynamic characteristics of the two mechanisms are compared. The performance of fish and vehicles with MPF is reviewed from the viewpoint of maneuverability. Especially, performance of a recently developed fish-like body with a pair of undulatory side fins, a model ship with a pair of ray-wing-type propulsors, and an underwater vehicle with two pairs of mechanical pectoral fins are discussed.