The variational point of view on exceptional structures in dimensions 6, 7 and 8 is one of Nigel Hitchin’s seminal contributions. One feature of this point of view is that it motivates the study of boundary value problems, for structures with prescribed data on a boundary. This chapter considers the case of 7 dimensions and G
2 structures. It briefly reviews a general framework and then goes on to examine in more detail symmetry reductions to dimensions 4 and 3. In the latter case, the chapter presents an interesting variational problem related to the real Monge–Ampère equation and describes a generalization of this.