  We survey some recent results on long-standing conjectures regarding Hamilton
cycles in directed graphs, oriented graphs and tournaments. We also combine
some of these to prove the following approximate result towards Kelly's
conjecture on Hamilton decompositions of regular tournaments: the edges of
every regular tournament can be covered by a set of Hamilton cycles which are
`almost' edge-disjoint. We also highlight the role that the notion of `robust
expansion' plays in several of the proofs. New and old open problems are
discussed.
