Nanoscale semiconductors with their unique properties and potential applications have been a focus of extensive research in recent years. There are many ways in which semiconductors change the world with computers, cell phones, and solar panels, and nanoscale semiconductors having a promising potential to expand the efficiency, reduce the cost, and improve the flexibility and durability of their design. In this study, theoretical quantum mechanical simulations were performed on several different nanoscale semiconductor materials, including graphene/phosphorene nanoribbons and group III-V nanowires. First principles density functional theory (DFT) was used to study the electronic and structural properties of these nanomaterials in their fully relaxed and strained states. The electronic band gap, effective masses of charge carriers, electronic orbitals, and density of states were most commonly examined with strain, both from intrinsic and external sources. For example, armchair graphene nanoribbons (AGNR) were found to have unprecedented band gap-strain dependence. Phosphorene nanoribbons (PNRs) demonstrate a different behavior, including a chemical scissors effect, and studies revealed a strong relationship between passivation species and band gap tunability. Unlike the super mechanical flexibility of AGNRs and PNRs which can sustain incredible strain, modest yet large strain was applied to group III-V nanowires such as GaAs/InAs. The calculations showed that a direct and indirect band gap transition occurs at some critical strains and the origination of these gap transitions were explored in detail. In addition to the pure nanowires, GaAs/InAs core/shell heterostructure nanowires were also studied. Due to the lattice mismatch between GaAs and InAs, the intrinsic strain in the core/shell nanowires demonstrates an interesting behavior on tuning the electronic properties. This interesting behavior suggests a mechanical way to exert compressive strain on nanowires experimentally, and can create a finite quantum confinement effect on the core.