A quantum confinement model for nanocrystals developed is extended to study for the optical gap shifts in core/shell quantum dots and nanowires. The chemical bond properties and gap shifts in the InP/ZnS, CdSe/CdS, CdSe/ZnS, and CdTe/ZnS core/shell quantum dots are calculated in detail. The calculated band gaps are in excellent agreement with experimental values. The effects of structural taping and twinning on quantum confinement of InP and Si nanowires are elucidated. It is found theoretically that a competition between the positive Kubo energy-gap shift and the negative surface energy shift plays the crucial role in the optical gaps of these nanosystems.