In this talk, I will report our research on basic reproduction ratio R0 for time-delayed compartmental population models in a periodic environment. It is proved that R0 serves as a threshold value for the stability of the zero solution of the associated periodic linear systems. In particular, we obtain an explicit formula of R0 for autonomous FDE models, which is a generalization of the van den Driessche-Watmough formula for ODE models. An extension of such a theory to spatial population models and a general algorithm for the numerical computation of R0 will be discussed. If time permits, I will also mention our more recent work on R0 for abstract FDE models with time-delayed internal transitions