Secondary aquatic vertebrates exhibit a diversity of swimming modes that use paired limbs and/or the tail. Various secondarily aquatic tetrapod clades, including amphibians, reptiles, and mammals use transverse undulations or oscillations of the tail for swimming. These movements have often been classified according to a kinematic gradient that was established for fishes but may not be appropriate to describe the swimming motions of tetrapods. To understand the evolution of movements and design of the tail in aquatic tetrapods, we categorize the types of tails used for swimming and examine swimming kinematics and hydrodynamics. From a foundation of a narrow, elongate ancestral tail, the tails used for swimming by aquatic tetrapods are classified as tapered, keeled, paddle, and lunate. Tail undulations are associated with tapered, keeled, and paddle tails for a diversity of taxa. Propulsive undulatory waves move down the tail with increasing amplitude toward the tail tip, while moving posteriorly at a velocity faster than the anterior motion of the body indicating that the tail is used for thrust generation. Aquatic propulsion is associated with the transfer of momentum to the water from the swimming movements of the tail, particularly at the trailing edge. The addition of transverse extensions and flattening of the tail increases the mass of water accelerated posteriorly and affects vorticity shed into the wake for more aquatically adapted animals. Digital Particle Image Velocimetry reveals that the differences were exhibited in the vortex wake between the morphological and kinematic extremes of the alligator with a tapering undulating tail and the dolphin with oscillating wing-like flukes that generate thrust. In addition to exploring the relationship between the shape of undulating tails and the swimming performance across aquatic tetrapods, the role of tail reduction or loss of a tail in aquatic-tetrapod swimming was also explored. For aquatic tetrapods, the reduction would have been due to factors including locomotor and defensive specializations and phylogenetic and physiological constraints. Possession of a thrust-generating tail for swimming, or lack thereof, guided various lineages of secondarily aquatic vertebrates into different evolutionary trajectories for effective aquatic propulsion (i.e., speed, efficiency, and acceleration).