Spermatozoa face the Herculean task of finding an egg and are beset with numerous challenges, not least reaching their target without getting lost. Furthermore, the sperm flagellum not only allows rapid swimming but also an ability to steer and thus navigate, invariably coupling sperm motility and guidance cue response. Thus in the following we briefly review the mechanics of how sperm swim, together with modelling strategies for developing computational simulations of swimming sperm. We proceed to consider how these simulations can inform our understanding of sperm guidance together with the limitations of modelling approaches, as well as perspectives of future studies that can be tackled with present modelling frameworks and where fundamental advances in our biological understanding are required for further progress.
Keywords: Boundary element method, Chemotaxis, Dynein regulation, Flagellar waveform, Hydrodynamics, Low Reynolds number, Mechanics, Modeling, Thigmotaxis, Numerical simulation, Regularized Stokeslet method, Resistive force theory, Rheotaxis, Slender-body theory, Stokes flow, Sperm swimming.