T-branes are bound states of ordinary D-branes, characterized by non-commuting expectation values for the worldvolume scalars. They defy usual geometric intuition and feature a variety of unconventional brane-model-building phenomena. In this talk I will discuss some general global properties of the vacuum solutions corresponding to T-branes, and show how supersymmetry puts strong constraints on the manifolds supporting them. Moreover, I will consider stability issues of such bound states at large volume, and give conditions to prevent their decay.