One-dimensional colloidal semiconductor nanowires are of wide interest in nanoscale electronics and photonics. As compared to the zero-dimensional counterparts, their geometrical anisotropy offers an additional degree of freedom to tailor the electronic and optical properties and enables customized heterostructures with increased complexity. The colloidal synthetic chemistry developed over past decades has fueled the emergence of diverse one-dimensional nanocrystals and heterostructures, whereas the synthetic pursuit for compositionally and structurally defining them at the atomic-level precision remains yet a giant challenge. Catalyzed growth, wherein nanowires grow at the catalyst-nanowire interfaces in a layer-by-layer manner, offers a promising path toward such an ultimate goal. In this Perspective, we will take a close look at how catalyzed growth would enable the on-demand, atomic-precision control of colloidal nanowires and their heterostructures. We then further highlight their potentials for constructing higher-order heteroarchitectures with new and/or enhanced performances. Finally, we conclude with a forward-looking perspective on future challenges.