  The Hajnal--Szemer\'edi theorem states that for any integer $r \ge 1$ and any
multiple $n$ of $r$, if $G$ is a graph on $n$ vertices and $\delta(G) \ge (1 -
1/r)n$, then $G$ can be partitioned into $n/r$ vertex-disjoint copies of the
complete graph on $r$ vertices. We prove a very general analogue of this result
for directed graphs: for any integer $r \ge 4$ and any sufficiently large
multiple $n$ of $r$, if $G$ is a directed graph on $n$ vertices and every
vertex is incident to at least $2(1 - 1/r)n - 1$ directed edges, then $G$ can
be partitioned into $n/r$ vertex-disjoint subgraphs of size $r$ each of which
contain every tournament on $r$ vertices. A related Tur\'an-type result is also
proven.
