One- and zero-dimensional organic/inorganic heterostructure materials have been attracting considerable attention in materials science because of their outstanding optical and electrical properties and high tailorability in terms of composition, structure, and morphology. Strong interactions between the organic and inorganic units can lead to novel or improved physical or chemical performance relative to that of the individual components, thereby realizing synergistic ("1 + 1 > 2") performance. In this tutorial review, we discuss the synthetic methods available for preparing heterostructures incorporating diverse components; the functionality of the heterostructure materials; and their potential applications in the fields of electronics, optics, biology, and catalysis. The future development of such heterostructure materials will require deeper understanding of organic-inorganic or organic-organic interfaces on the nanoscale, collective phenomena, and interparticle coupling.