The propelling modes utilizing the long-fin undulations are considered having great potential for exploiting the future underwater vehicles. The biological background and mathematical analysic methods of the underwater biomimetic propulsor employing the long-undulating-fin are presented. The achievements and the current situation of the researches on the underwater long-undulating-fin propulsor at home and abroad are generally summarized. The control problems which must be solved by the underwater biomimetic propulsor are tersely discussed. The challenges faced by the propulsive system control are state keeping under serious perturbations, rapid maneuvering, power-efficient endurance swimming, and trajectory planning and tracking. The design and control of the underwater biomimetic propulsors taking up these challenges will require state-of-the-art engineering and biology.