We’ll recall the definition of Bridgeland’s stability conditions and of the stability manifold. Most of the work on this subject focuses on the derived category of a smooth projective variety, because of technical difficulties in approaching singular varieties. To bypass singularities, we look at stability conditions on the derived category of smooth stacks instead. We’ll construct stability conditions on orbifolds, and focus on the example of a root stack. In this case, there is an interesting correspondence between wall-crossing on the stability manifold and moduli spaces of parabolic bundles.