The authors employ three numerical methods to explore the motion of low Reynolds number swimmers, modeling 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, the authors are able to compare and assess the effectiveness of the different approaches. They then propose a new class of low Reynolds number swimmers, generalized three bead swimmers that can change both the length of their arms and the angle between them. Hence they suggest a design for a microstructure capable of moving in three dimensions. They discuss multiple bead, linear microstructures and show that they are highly efficient swimmers. They then turn to consider the swimming motion of elastic filaments. Using multiparticle collision dynamics the authors show that a driven filament behaves in a qualitatively similar way to the micron-scale swimming device recently demonstrated by Dreyfus et al. [Nature (London) 437, 862 (2005)]. (c) 2007 American Institute of Physics.