The topic of the talk will be Floer theories on exact symplectic orbifolds with smooth contact boundary. More precisely, I will first describe the construction, which only uses classical transversality techniques, of a symplectic cohomology group on such symplectic orbifolds. Then, I will give some geometrical applications, such as restrictions on possible singularities of exact symplectic fillings of some particular contact manifolds, and the existence, in any odd dimension at least 5, of a pair of contact manifolds with no exact symplectic (smooth) cobordisms in either direction. This is joint work with Zhengyi Zhou.