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Let $\mathcal{OG}(4)$ denote the family of all graph-group pairs $(\Gamma,G)$where $\Gamma$ is 4-valent, connected and $G$-oriented($G$-half-arc-transitive). Using a novel application of the structure theoremfor biquasiprimitive permutation groups of the second author, we produce adescription of all pairs $(\Gamma, G) \in\mathcal{OG}(4)$ for which everynontrivial normal subgroup of $G$ has at most two orbits on the vertices of$\Gamma$. In particular we show that $G$ has a unique minimal normal subgroup$N$ and that $N \cong T^k$ for a simple group $T$ and $k\in \{1,2,4,8\}$. Thisprovides a crucial step towards a general description of the long-studiedfamily $\mathcal{OG}(4)$ in terms of a normal quotient reduction. We also giveseveral methods for constructing pairs $(\Gamma, G)$ of this type and providemany new infinite families of examples, covering each of the possiblestructures of the normal subgroup $N$.

Four-Valent Oriented Graphs of Biquasiprimitive Type