  In this survey we overview known results and get several new results on
digraph compositions which generalize several classes of digraphs, such as
quasi-transitive digraphs. After an introductory section, the paper is divided
into six sections: connectivity and linkages, kings and kernels, paths, cycles,
acyclic spanning subdigraphs, strong spanning subdigraphs. This survey also
contains some conjectures and open problems for further study.
