Depending upon the underlying assumptions and reason for including delay in a model of population growth, different strategies for deriving the models will be discussed. Discrete delay differential equations, integro-differential equations and difference equations with both discrete and distrbuted delay will be considered. In all cases the delay is included in the growth of the population consistent with the decline of the population predicted by the model so that those contributing to the growth survive the delay period. In each case there is an important critical delay threshold that depends on the length of the delay and other parameters in the model. If the length of the time delay exceeds this threshold, the models predict that the population will go extinct for any non-negative initial conditions. Below this threshold, there is at least one positive equilibrium. The number of positive equilibria, their stability, and how their magnitude depends on the length of the delay will be discussed.