In this work we review the aggregation of variables method for discrete dynamical
systems. These methods consist of describing the asymptotic behaviour of a complex system
involving many coupled variables through the asymptotic behaviour of a reduced system
formulated in terms of a few global variables. We consider population dynamics models
including two processes acting at different time scales. Each process has associated a map
describing its effect along its specific time unit. The discrete system encompassing both
processes is expressed in the slow time scale composing the map associated to the slow one
and the k-th iterate of the map associated to the fast one. In the linear case a result is
stated showing the relationship between the corresponding asymptotic elements of both
systems, initial and reduced. In the nonlinear case, the reduction result establishes the
existence, stability and basins of attraction of steady states and periodic solutions of
the original system with the help of the same elements of the corresponding reduced
system. Several models looking over the main applications of the method to populations
dynamics are collected to illustrate the general results.