We use three numerical methods to explore the motion of low Reynolds number swimmers, modelling the hydrodynamic interactions by means of the Oseen tensor approximation, lattice Boltzmann simulations and multiparticle collision dynamics. By applying the methods to a three bead linear swimmer, for which exact results are known, we are able to compare and assess the effectiveness of the different approaches. We use the algorithms to explore the interactions between swimmers. We shall also discuss a continuum model for swimmers which shows a rich rheology and point out the current gap between explicitly modelling individual swimmers and the continuum approach.