We consider nanostructures that consist of both organic and inorganic materials, in particular, heterojunctions or microcavities. When resonance between the Wannier and Frenkel excitons is realized, their coupling (through the Coulomb dipole-dipole interaction at an interface or via exchange of cavity photons in coupled microcavities) leads to novel striking effects. First, we discuss the properties of the hybrid Frenkel-Wannier excitons that appear when the energy splitting of the excitonic spectrum is large compared to the exciton linewidths (the case of strong resonant coupling). We show that the new hybrid states and their dispersion curves can be tailored to engineer the enhancement of resonant optical nonlinearities, fluorescence efficiency, and relaxation processes. Next, we consider the case of weak resonant coupling for which the Förster mechanism of energy transfer from an inorganic quantum well to an organic overlayer is of great interest: the electrical pumping of excitons in the semiconductor quantum well could be employed to efficiently turn on the organic material luminescence. In both weak and strong coupling regimes, the properties of the molecular and covalent crystalline layers conspire to overcome the basic limitations of the individual constituents.