Heteroepitaxy-atomically aligned growth of a crystalline film atop a different crystalline substrate-is the basis of electrically driven lasers, multijunction solar cells, and blue-light-emitting diodes. Crystalline coherence is preserved even when atomic identity is modulated, a fact that is the critical enabler of quantum wells, wires, and dots. The interfacial quality achieved as a result of heteroepitaxial growth allows new combinations of materials with complementary properties, which enables the design and realization of functionalities that are not available in the single-phase constituents. Here we show that organohalide perovskites and preformed colloidal quantum dots, combined in the solution phase, produce epitaxially aligned 'dots-in-a-matrix' crystals. Using transmission electron microscopy and electron diffraction, we reveal heterocrystals as large as about 60 nanometres and containing at least 20 mutually aligned dots that inherit the crystalline orientation of the perovskite matrix. The heterocrystals exhibit remarkable optoelectronic properties that are traceable to their atom-scale crystalline coherence: photoelectrons and holes generated in the larger-bandgap perovskites are transferred with 80% efficiency to become excitons in the quantum dot nanocrystals, which exploit the excellent photocarrier diffusion of perovskites to produce bright-light emission from infrared-bandgap quantum-tuned materials. By combining the electrical transport properties of the perovskite matrix with the high radiative efficiency of the quantum dots, we engineer a new platform to advance solution-processed infrared optoelectronics.