For a positive integer k, we say a simple graph G is a k-circulant if it admits a semiregular automorphism that partitions its vertex-set into k orbits of the same size. The study of k-circulant graphs is extensive, specially that of vertex- and arc-transitive ones, and some families of k-circulants, for small values of k, are of particular interest. We provide a complete classification, along with some structural results, for cubic vertex-transitive 3-circulants.