A somewhat detailed discussion of mappings between apparently different physical systems is presented. The main idea is that by establishing these mappings one may obtain a better understanding of one system from available information on the other, with the ideal situation that by choosing appropriately a description of a system we may transform it to another where a solution is easier or even exact. Several mappings are considered from mappings between classical and quantum systems as one changes the space dimensionality to mappings between spin systems and bosonic or fermionic systems. One example is a duality between a two-dimensional classical spin problem, specifically an Ising model, and the one-dimensional quantum Ising model in a transverse field, solvable in some appropriate way, here discussed. Different representations of spin operators are considered and complex interacting systems are represented exactly by different systems for which an exact solution or some approximate solution that is better controlled are available.