A major puzzle in biology is how mammalian sperm cells determine and maintain the correct swimming direction during the various phases of the sexual reproduction process. Currently debated mechanisms for sperm long range travel vary from peristaltic pumping to temperature sensing (thermotaxis) and direct response to fluid flow (rheotaxis), but little is known quantitatively about their relative importance. Here, I will discuss an experimental study of mammalian sperm navigation along structured surfaces and under a fluid flow. Using microfluidic devices, one can investigate systematically the swimming behaviour of human and bull sperm over a wide range of physiologically relevant shear rates and viscosities. The measurements show that the interplay of fluid shear, steric surface-interactions and chirality of the flagellar beat leads to a stable upstream spiralling motion of sperm cells, thus providing a generic and robust rectification mechanism to support mammalian fertilization. Additionally, the very recent findings on spermatozoa trajectories in periodic flow suggest two distinct modes sperm sub-population dynamics. I will also discuss collective phenomena in suspensions of swimming cells.