Quantum materials are usually heterogeneous, with structural defects, impurities, surfaces, edges, interfaces, and disorder. These heterogeneities are sometimes viewed as liabilities within conventional systems; however, their electronic and magnetic structures often define and affect the quantum phenomena such as coherence, interaction, entanglement, and topological effects in the host system. Therefore, a critical need is to understand the roles of heterogeneities in order to endow materials with new quantum functions for energy and quantum information science applications. In this article, several representative examples are reviewed on the recent progress in connecting the heterogeneities to the quantum behaviors of real materials. Specifically, three intertwined topic areas are assessed: i) Reveal the structural, electronic, magnetic, vibrational, and optical degrees of freedom of heterogeneities. ii) Understand the effect of heterogeneities on the behaviors of quantum states in host material systems. iii) Control heterogeneities for new quantum functions. This progress is achieved by establishing the atomistic-level structure-property relationships associated with heterogeneities in quantum materials. The understanding of the interactions between electronic, magnetic, photonic, and vibrational states of heterogeneities enables the design of new quantum materials, including topological matter and quantum light emitters based on heterogenous 2D materials.