Cytoplasmic dynein is an important motor that drives all minus-end directed movement along microtubules. Dynein is a complex motor whose processive motion is driven by ATP-hydrolysis. Dynein's run length has been measured to be several millimetres with typical velocities in the order of a few nanometres per second. Therefore, the average time between steps is a fraction of a second. When this time scale is compared with typical time scales for protein side chain and backbone movements (approximately 10(-9) s and approximately 10(-5) s, respectively), it becomes clear that a multi-timescale modelling approach is required to understand energy transduction in this protein. Here, we review recent efforts to use computational and mathematical modelling to understand various aspects of dynein's chemomechanical cycle. First, we describe a structural model of dynein's motor unit showing a heptameric organization of the motor subunits. Second, we describe our molecular dynamics simulations of the motor unit that are used to investigate the dynamics of the various motor domains. Third, we present a kinetic model of the coordination between the two dynein heads. Lastly, we investigate the various potential geometries of the dimer during its hydrolytic and stepping cycle.