The spermatozoon must find its female gamete partner and deliver its genetic material to generate a new individual. This requires that the spermatozoon be motile and endowed with sophisticated swimming strategies to locate the oocyte. A common strategy is chemotaxis, in which spermatozoa detect and follow a gradient of chemical signals released by the egg and its associated structures. Decoding the female gamete's positional information is a process that spermatozoa undergo in a three-dimensional (3D) space; however, due to their speed and small size, this process has been studied almost exclusively in spermatozoa restricted to swimming in two dimensions (2D). This review examines the relationship between the mechanics of sperm propulsion and the physiological function of these cells in 3D. It also considers whether it is possible to derive all the 3D sperm swimming characteristics by extrapolating from 2D measurements. It is concluded that full insight into flagellar beat dynamics, swimming paths and chemotaxis under physiological conditions will eventually require quantitative imaging of flagellar form, ion flux changes, cell trajectories and modelling of free-swimming spermatozoa in 3D.