We study dynamic task allocation when service providers’ expertise evolves. Clients arrive sequentially seeking service. Seniors provide superior service but entail waiting in a queue, which progresses at a speed dependent on their volume. Juniors offer service without wait and become seniors with experience. We show that clients choose senior service too frequently, generating longer waits and little training relative to the social optimum. Welfare gains from centralization are greater for larger institutions, better training technologies, and lower waiting costs. Finally, monitoring the seniors’ queue increases welfare but may decrease training. Methodologically, we explore a matching setting in which agents’ types are endogenous, and illustrate the usefulness of queueing theory techniques.