Delay equations arise naturally in models of populations whose growth rate depends on a variable that requires some time to begin interacting. Some examples include the time until sexual maturity is reached in animal species, or the incubation period of a virus. In the talk I will present recent results on the characterization and stability of periodic solutions in a particular class of delay equations. A special case treated in the presentation includes the characterization of globally attracting periodic solutions in a population whose growth is negatively affected by a thriving state at a past time.