Undulatory underwater swimming (UUS) occurs in the starts and turns of three of the four competitive swimming strokes and plays a significant role in overall swimming performance. The majority of research examining UUS is comparative in nature, dominated by studies comparing aquatic animals' undulatory locomotion with the UUS performance of humans. More recently, research directly examining human forms of UUS have been undertaken, providing further insight into the factors which influence swimming velocity and efficiency. This paper reviews studies which have examined the hydromechanical, biomechanical, and coordination aspects of UUS performance in both animals and humans. The present work provides a comprehensive evaluation of the key factors which combine to influence UUS performance examining (1) the role of end-effector frequency and body amplitudes in the production of a propulsive waveform, (2) the effects of morphology on the wavelength of the propulsive waveform and its subsequent impact on the mode of UUS adopted, and (3) the interactions of the undulatory movements to simultaneously optimise propulsive impulse whilst minimising the active drag experienced. In conclusion, the review recommends that further research is required to fully appreciate the complexity of UUS and examine how humans can further optimise performance.