We establish the general machinery of string topology for differentiable stacks applying to both free loops in stacks and hidden loops. In particular, we construct a bivariant theory for topological stacks providing us with a flexible theory of Gysin maps. We prove that the homology of the free loop stack of an oriented stack and the homology of hidden loops are compatible Frobenius algebras. We also prove that the homology of free loop stack has a natural structure of BV-algebra, which is part of an homological conformal field theories with closed positive boundaries. We construct an intersection pairing for almost complex orbifolds Poincaré dual of Chen-Ruan orbifold cup-product. Finally we gave some examples including the case of the classifying stacks of a compact Lie group.