We will generalize the theory of topological insulators and superconductors to account for topological defects. We develop a unified framework to topologically classify point and line defects in insulators and superconductors described by spatially modulated Bloch and Bogoliubov de Gennes Hamiltonians. By a generalization of the bulk boundary correspondence, these defects are associated with topologically protectedelectronic states. Many examples will be discussed, including 1D chiral Dirac fermion states, which can exist in 3D magnetic topological insulator structures and 0D Majorana fermion bound states that can occur in 3D topological insulator superconductor structures. The latter exhibit a 3D generalization of non-Abelian statistics.