Approximations are used for dealing with problems that are hard. In this talk, we introduce the concepts relating to the approximation of Propositional Classical Logic with a family of Logics. We do not deal with logics that give answers “approximately correct” such as Fuzzy or Multivalued Logics, but with families of logics that, in the limit, tend to Classical Logic. It also happens that approximated reasoning plays an important role in modelling non-ideal agents. Real agents (natural or artificial) are limited in their reasoning capabilities. We present a general framework for modelling limited reasoning based on approximate reasoning and discuss its properties. The original ideas from which this approach developed were proposed by Cadoli and Schaerf. Unfortunately, their proposal had limitations, both in the expressivity of the language as well as in the inexistence of an incremental method to perform the approximations. Our work has focused on solving these defficiencies, and in understanding some interesting phenomena that we uncover in this process, such as the balance between expressivity vs control of approximations. Some open problems and discussed at the end.