We consider the dynamics of dust and gas during the clearing of protoplanetary discs. We work within the context of a photoevaporation/viscous model for the evolution of the gas disc, and use a two-fluid model to study the dynamics of dust grains as the gas disc is cleared. Small (<~10um) grains remain well-coupled to the gas, but larger (~1mm) grains are subject to inward migration from large radii (~50AU), suggesting that the time-scale for grain growth in the outer disc is ~10^4-10^5yr. We describe in detail the observable appearance of discs during clearing, and find that pressure gradients in the gas disc result in a strong enhancement of the local dust-to-gas ratio in a ring near to the inner disc edge. Lastly, we consider a simple model of the disc-planet interaction, and suggest that observations of disc masses and accretion rates provide a straightforward means of discriminating between different models of disc clearing.