In engineering applications, simulations involving heterogeneous materials where it is necessary to capture the local response coming from the heterogeneities is very difficult. The use of homogenization techniques can reduce the size of the problem but will miss the local effects. Homogenization can also be difficult if the constituents obey different constitutive laws. Additional complications arise if inelastic deformation occurs. In such cases a two-scale approach is preferred and this work addresses these issues in the context of a two-scale Finite Element Method (FEM). Examples of using two-scale FEM approaches are presented.