Regeneration is a complex and dynamic process, mobilizing diverse cell types and remodelling tissues over long time periods. Tracking cell fate and behaviour during regeneration in active adult animals is especially challenging. Here, we establish continuous live imaging of leg regeneration at single-cell resolution in the crustacean Parhyale hawaiensis. By live recordings encompassing the first 4-5 days after amputation, we capture the cellular events that contribute to wound closure and morphogenesis of regenerating legs with unprecedented resolution and temporal detail. Using these recordings we are able to track cell lineages, to generate fate maps of the blastema and to identify the progenitors of regenerated epidermis. We find that there are no specialized stem cells for the epidermis. Most epidermal cells in the distal part of the leg stump proliferate, acquire new positional values and contribute to new segments in the regenerating leg.