Anisotropic heterostructures of colloidal nanocrystals embed size-, shape-, and composition-dependent electronic structure within variable three-dimensional morphology, enabling intricate design of solution-processable materials with high performance and programmable functionality. The key to designing and synthesizing such complex materials lies in understanding the fundamental thermodynamic and kinetic factors that govern nanocrystal growth. In this review, nanorod heterostructures, the simplest of anisotropic nanocrystal heterostructures, are discussed with respect to their growth mechanisms. The effects of crystal structure, surface faceting/energies, lattice strain, ligand sterics, precursor reactivity, and reaction temperature on the growth of nanorod heterostructures through heteroepitaxy and cation exchange reactions are explored with currently known examples. Understanding the role of various thermodynamic and kinetic parameters enables the controlled synthesis of complex nanorod heterostructures that can exhibit unique tailored properties. Selected application prospects arising from such capabilities are then discussed.