1 Introduction
1.1 Digraph compositions and related digraph classes
1.2 Further notation and terminology
2 Connectivity and linkages
2.1 Connectivity
2.2 Linkages
3 Kings and kernels
3.1 Kings
3.2 Kernels
4 Paths
4.1 Hamiltonian paths
4.2 Path subdigraphs
4.3 Path partition conjecture
5 Cycles
5.1 Hamiltonian cycles
5.2 Pancyclicity
5.3 Cycle factors
6 Acyclic spanning subdigraphs
6.1 The existence of prescribed acyclic spanning subdigraphs
6.2 Arc-disjoint in-and out-branchings
7 Strong spanning subdigraphs
7.1 Strong spanning subdigraphs without a 2-cycle
7.2 Smallest strong spanning subdigraph
7.3 Strong arc decomposition