We review the current state of the theory of large-scale structure in a warm dark matter (WDM) cosmological model. In particular, we focus on the non-linear modelling of the matter power spectrum and on the mass function of dark matter haloes. We describe the results of N-body simulations with WDM and mention the effects that could be induced by baryonic physics. We also examine the halo model of large-scale structure and its recently suggested modifications for a WDM cosmology, which account for the small-scale smoothness of the initial matter density field and better fit the results of N-body simulations. Having described the theoretical models, we discuss the current lower limits on the WDM particle mass, m wdm, which correspond to upper limits on the WDM temperature under the assumption that the particles are thermal relics. The best such constraints come from the Lyα forest and exclude all masses below 3.3 keV at the 2σ confidence level. We finally review the forecasts for future lensing surveys, which will be of the same order of magnitude as the already existing constraints from the Lyα forest data but explore a different redshift regime.