Discretisation of linear parameter-varying (LPV) systems is a relevant, but insufficiently investigated problem of both LPV control design and system identification. In this contribution, existing results on the discretisation of LPV state-space models with static dependence (without memory) on the scheduling signal are surveyed and new methods are introduced. These approaches are analysed in terms of approximation error, considering ideal zero-order hold actuation and sampling of the input-output signals and scheduling variables of the system. Criteria to choose appropriate sampling periods with respect to the investigated methods are also presented. The application of the considered approaches on state-space representations with dynamic dependence (with memory) on the scheduling is investigated in a higher-order hold sense.