A digraph (that is a directed graph) is said to be highly arc transitive if its automorphism group is transitive on the set ofs-arcs for eachs≥0. Several new constructions are given of infinite highly arc transitive digraphs. In particular, for Δ a connected, 1-arc transitive, bipartite digraph, a highly arc transitive digraphDL(Δ) is constructed and is shown to be a covering digraph for every digraph in a certain classD(Δ) of connected digraphs. Moreover, if Δ is locally finite, thenDL(Δ) is a universal covering digraph forD(Δ). Further constructions of infinite highly arc transitive digraphs are given.