  The modern theory of homogeneous structures begins with the work of Roland
Fra\"iss\'e. The theory developed in the last seventy years is placed in the
border area between combinatorics, model theory, algebra, and analysis. We turn
our attention to its combinatorial pillar, namely, the work on the
classification of structures for given homogeneity types, and focus onto the
homomorphism homogeneous ones, introduced in 2006 by Cameron and
Ne\v{s}et\v{r}il. An oriented graph is called homomorphism homogeneous if every
homomorphism between finite induced subgraphs extends to an endomorphism. In
this paper we present a complete classification of the countable homomorphism
homogeneous oriented graphs.
