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