Fully developed flow in an infinite helically coiled pipe is studied, motivated by physiological applications. Most of the bends in the mammalian arterial system curve in a genuinely three-dimensional way, so that the arterial centreline has not only curvature but torsion and can be modelled by a helix. Flow in a helically symmetric pipe generalizes related problems in axisymmetry (Dean flow) and two-dimensionality, but the geometry ensures that even irrotational flow has a cross-pipe component. Fully developed helical flows driven by a steady pressure gradient are studied analytically and numerically. Varying the radius and pitch of the helical pipe, the effects of curvature and torsion on the flow are investigated.