In this chapter, we study the structure of C¹ interiors of some basic sets of dynamical systems having various shadowing properties. We give either complete proofs or schemes of proof of the following main results: • The C¹ interior of the set of diffeomorphisms having the standard shadowing property is a subset of the set of structurally stable diffeomorphisms (Theorem 3.1.1); this result and Theorem 1.4.1 (a) imply that the C¹ interior of the set of diffeomorphisms having the standard shadowing property coincides with the set of structurally stable diffeomorphisms; • the set Int1.OrientSPF n B/ is a subset of the set of structurally stable vector fields (Theorem 3.3.1); similarly to the case of diffeomorphisms, this result and Theorem 1.4.1 (b) imply that the set Int1.OrientSPF n B/ coincides with the set of structurally stable vector fields; • the set Int1.OrientSPF/ contains vector fields that are not structurally stable (Theorem 3.4.1).