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We survey results concerning various generalizations of tournaments. The reader will see that tournaments are by no means the only class of directed graphs with a very rich structure. We describe, among numerous other topics mostly related to paths and cycles, results on hamiltonian paths and cycles. The reader will see that although these problems are polynomially solvable for all of the classes described, they can be highly nontrivial, even for these “tournament‐like” digraphs. © 1998 John Wiley & Sons, Inc. J. Graph Theory 28: 171–202, 1998