Vertex-quasiprimitive 2-arc-transitive digraphs

We study vertex-quasiprimitive 2 -arc-transitive digraphs, and reduce the problem of vertex-primitive 2 -arc-transitive digraphs to almost simple groups. This includes a complete classification of vertex-quasiprimitive 2 -arc-transitive digraphs where the action on vertices has O’Nan-Scott type SD or CD.