Seven-manifolds with a G2-structure possess two distinguished classes of submanifolds: associative 3-folds and coassociative 4-folds. When the G2-structure is torsion-free, such submanifolds are minimal (in fact, calibrated) and exist locally. We are led to ask: For which classes of G2-structures is it the case that associative 3-folds (respectively, coassociative 4-folds) are always minimal submanifolds? We will answer this by deriving a simple formula for the mean curvature, in the process uncovering new obstructions to the local existence of coassociatives. Time permitting, we will discuss the analogous results for special Lagrangian 3-folds (respectively Cayley 4-folds) in 6-manifolds with SU(3)-structures (respectively 8-manifolds with Spin(7)-structures). This is joint work with Gavin Ball.