Stochastic models of populations have a long history beginning with branching processes and continuing with models in population genetics and models of the spatial distribution of populations. At the same time, models of population genealogies were developed in the population genetics literature. Work with Peter Donnelly (1999) showed how to simultaneously construct models that include both the forward in time evolution of the population distribution and the backward in time genealogy starting at any time point in the forward in time evolution. These "lookdown" constructions were essentially restricted to neutral models, that is, models in which birth rates, offspring distributions, and death rates do not depend on the types or locations of the individuals in the population. Following some earlier preliminary results, work with Eliane Rodrigues (2011) gave lookdown constructions for general Markov branching processes in which the birth rates, offspring distributions, and death rates can depend on the location/type of the individual. Extension of these lookdown/genealogical constructions to very general Markov population models, to appear in a forthcoming paper with Alison Etheridge, will be discussed.