Semiconducting nanowires offer the possibility of nearly unlimited complex bottom-up design, which allows for new device concepts. However, essential parameters that determine the electronic quality of the wires, and which have not been controlled yet for the III-V compound semiconductors, are the wire crystal structure and the stacking fault density. In addition, a significant feature would be to have a constant spacing between rotational twins in the wires such that a twinning superlattice is formed, as this is predicted to induce a direct bandgap in normally indirect bandgap semiconductors, such as silicon and gallium phosphide. Optically active versions of these technologically relevant semiconductors could have a significant impact on the electronics and optics industry. Here we show first that we can control the crystal structure of indium phosphide (InP) nanowires by using impurity dopants. We have found that zinc decreases the activation barrier for two-dimensional nucleation growth of zinc-blende InP and therefore promotes crystallization of the InP nanowires in the zinc-blende, instead of the commonly found wurtzite, crystal structure. More importantly, we then demonstrate that we can, once we have enforced the zinc-blende crystal structure, induce twinning superlattices with long-range order in InP nanowires. We can tune the spacing of the superlattices by changing the wire diameter and the zinc concentration, and we present a model based on the distortion of the catalyst droplet in response to the evolution of the cross-sectional shape of the nanowires to quantitatively explain the formation of the periodic twinning.