  A conjecture of Jackson from 1981 states that every $d$-regular oriented
graph on $n$ vertices with $n\leq 4d+1$ is Hamiltonian. We prove this
conjecture for sufficiently large $n$. In fact we prove a more general result
that for all $\alpha>0$, there exists $n_0=n_0(\alpha)$ such that every
$d$-regular digraph on $n\geq n_0$ vertices with $d \geq \alpha n $ can be
covered by at most $n/(d+1)$ vertex-disjoint cycles, and moreover that if $G$
is an oriented graph, then at most $n/(2d+1)$ cycles suffice.
