Using semiconductor nanocrystals (NCs) one can produce extremely strong spatial confinement of electronic wave functions not accessible with other types of nanostructures. As a result, NCs exhibit important physical properties which, in combination with the chemical stability and solution processability, make this class of functional materials particularly appealing for several technological fields, such as solid-state lighting, lasers, photovoltaics, and electronics. Generally, the tunability of their physical properties is achieved through particle-size control of the quantum confinement effect. Wavefunction engineering adds a degree of freedom for manipulating the physical properties of NCs by selectively confining the carriers in specific domains of the material, thereby controlling the spatial overlap between the electron and hole wavefunctions. This design has been applied to several material systems in different geometries and has been shown to successfully control the emission energy and recombination dynamics as well as to reduce nonradiative Auger recombination, a process in which, as a consequence of strong spatial confinement, the energy of one electron-hole pair is nonradiatively transferred to a third charge carrier. The focus of this presentation is on nanocrystal heterostructures that comprise a small CdSe core overcoated with a thick shell of wider-gap CdS. These quasi-type II structures show greatly suppressed Auger recombination, which allows us to realize broadband optical gain (extends over 500 meV), and are a remarkable class of model compounds for investigating the influence of nanoengineered electron-hole overlap on the exciton fine structure. We indeed recently showed that this quasi-type II motif can be used to tune the energy splitting between optically active ("bright") and optically passive ("dark") excitons due to strong electron-hole exchange interaction, which is typical of quantum-confined semiconductor nanocrystals. This design provides a new tool for controlling excitonic dynamics including absolute recombination time scales and temperature and magnetic field dependences separately from the confinement energy. As a result of reduced Auger recombination, in combination with essentially complete suppression of energy-transfer in thick-shell NCs films, we recently fabricated bright, monochrome LEDs based on these nanostructures. Our results indicate that the luminance and efficiency can be improved dramatically by increasing the shell thickness without detrimental effects of increased turn-on voltage. Detailed structural and spectroscopic studies reveal a crucial role of interfaces on the Auger recombination process ion these heterostructures. Specifically, we observe a sharp transition to Auger-recombination-free behavior for shell thickness ∼1.8-2.5 nm, accompanied by the development of an intense phonon mode characteristic of a CdSeS alloy. These results suggest that the likely reason for suppressed Auger recombination in these nanostructures is the "smoothing out" of the otherwise sharp confinement potential due to formation of a graded interfacial CdSeS layer between the CdSe core and the CdS shell, as was recently proposed by theoretical calculations by Cragg and Efros.