The purpose of this paper is to present the new version of GEMINI-E3, which is the fifth and incorporates significant changes from the previous version in particular with respect to its size and its modularity. GEMINI-E3 is a Computable General Equilibrium Model and represents now a family of models of different specifications and with several successive versions. It retains many specifications that are common to CGE models but also some specific features, mainly concerning the measurement and analysis of the welfare cost of policies and the great detail in the representation of taxation and social security contributions. The paper gives a detailed presentation of the model, its main blocks and equations, and shows how it can be adapted to specific contexts. In particular a new version is being developed jointly with the standard one, taking into account the constraints of the European Monetary Union and the unbalances in the labor markets of industrialized countries (GEMINI-EMU). This clearly shows that CGE models, beside their main virtue that is total consistency at the domestic and at the world levels, are very flexible in their specification.