Semiconductor nanowires show promise for use in nanoelectronics, fundamental electron transport studies, quantum optics and biological sensing. Such applications require a high degree of nanowire growth control, right down to the atomic level. However, many binary semiconductor nanowires exhibit a high density of randomly distributed twin defects and stacking faults, which results in an uncontrolled, or polytypic, crystal structure. Here, we demonstrate full control of the crystal structure of InAs nanowires by varying nanowire diameter and growth temperature. By selectively tuning the crystal structure, we fabricate highly reproducible polytypic and twin-plane superlattices within single nanowires. In addition to reducing defect densities, this level of control could lead to bandgap engineering and novel electronic behaviour.