I will discuss important sub-structure that arises in the supersymmetric moduli space of heterotic theories. Smooth heterotic theories typically only admit supersymmetric gauge configurations in a part their Kahler cone and the presence of boundary walls between supersymmetric and non-supersymmetric regions can have significant phenomenological effects. Specifically, I will discuss heterotic supersymmetry and vector bundle slope stability from an effective field theory point of view and discuss physical applications of this description including branch structure which allows for transitions between effective theories, constraints on yukawa couplings and supersymmetry breaking.