After reviewing different strategies for deriving multi-species discrete mathematical models, a new strategy is proposed and then used to derive a predator–prey model and a model of competition between two populations. It is shown why phase-plane analysis of planar maps has not been as useful as it has been for planar systems of ordinary differential equations. To rectify this issue we introduce the next-iterate operator associated with the nullclines and their associated root-curves. The root-curves determine on which side of the associated nullcline the next iterate lies. How to use the phase portrait augmented with the root-curves, to determine both local and global properties of discrete planar models, is demonstrated. This provides an elementary approach that can be applied to help determine properties of the dynamics of planar discrete models. (This is joint work with Sabrina Streipert).