Interfacial energy functionals are ubiquitous in nature. However, some of the most basic questions are still open. In this talk, I will address one of these questions and characterize local minimizers of the interface energy. We'll establish that regular flat partitions are locally minimizing the interface energy with respect to L^1 perturbations of the phases. Regular flat partitions are partitions of open sets in the plane whose network of interfaces consists of finitely many straight segments with a singular set made up of finitely many triple junctions at which the Herring angle condition is satisfied. The proof relies on a localized version of the paired calibration method which was introduced by Lawlor and Morgan (Pac. J. Appl. Math., 166(1), 1994) in conjunction with a relative energy functional that precisely captures the suboptimality of classical calibration estimates. Vice versa, we show that any stationary point of the length functional (in a sense of metric spaces) must be a regular flat partition. This is joint work with J. Fischer, S. Hensel, and T. Simon.