Asymptotic variational methods are aimed at describing the overall properties of an increasingly complicated system by computing an effective limit energy where some parameters are averaged out or greatly simplified. Such methods include Gamma-convergence and variational expansions. An extremely interesting field of application is that of discrete (lattice) systems, where the determination of the relevant parameters in the limit theory is part of the problem. I will present an overview of the Gamma-convergence methods and a few examples that range from nonlinear discrete homogenization to expansions in fracture mechanics to size effects in thin films to variational percolation problems.