  We review some results on abstract linear and nonlinear population models
with age and spatial structure. The results are mainly based on the assumption
of maximal $L_p$-regularity of the spatial dispersion term. In particular, this
property allows us to characterize completely the generator of the underlying
linear semigroup and to give a simple proof of asynchronous exponential growth
of the semigroup. Moreover, maximal regularity is also a powerful tool in order
to establish the existence of nontrivial positive equilibrium solutions to
nonlinear equations by fixed point arguments or bifurcation techniques. We
illustrate the results with examples.
