In the following two former sections, we introduce the complexity for the decision versions of ISSP or/and ASSP on general digraphs, semicomplete digraphs, symmetric digraphs and Eulerian digraphs. Inapproximability results on ISSP and ASSP are mentioned in Sect. 4.3. The last section, Sect. 4.4, is about two related topics. The first one includes Kriesell conjecture and its extension in strong subgraph packing problem, and the second one concerns a new connectivity on digraphs, strong subgraph connectivity.