To reveal oscillatory fluctuations observed in the blowfly population, Gurney et al. proposed a model described by a delay differential equation. This model and its modifications, referred to as Nicholson’s blowflies equations, have also been used to describe population growth of other species and hence have been extensively and intensively studied. In this talk, we present some results on these equations. Most of them are related to stability. First, we consider the local dynamics. Then we consider the effects of spatial diffusion. This main part is our recent work on global dynamics of delayed reaction-diffusion equations in unbounded domains.