Energy-driven pattern formation is difficult to define, but easy to recognize. I'll discuss two examples: (a) cross-tie wall patterns in magnetic thin films. (b) surface-energy-driven coarsening of two-phase mixtures. The two problems are rather different -- the first is static, the second dynamic. But they share certain features: in each case nature forms complex patterns as it attempts to minimize a suitable "free energy". The task of modeling and analyzing such patterns is a rich source of challenges -- many still open -- in the multidimensional calculus of variations.