Growth and luminescence properties of InN nanobelts (InNNBs) and InGaN nanowires (NWs) by MOCVD and thermal CVD will be presented, along with their relation and difference to thin film counterparts. While there is a growing acceptance of the low band gap (0.6-0.7 eV) of InN, the optical properties of the actual samples still suffered, presumably due to the difficulty in obtaining high-quality samples and/or controlling their defect and carrier concentrations. However, the free-standing nanobelts can be nearly defect-free, allowing an excellent opportunity for fundamental investigations on unique dimensionality. InNNBs show photoluminescence (PL) in IR with peak width of 14 meV, the sharpest reported to date for InN. Interestingly, with increasing excitation intensity, InNNBs reveal an anomalously large blueshift in PL, compared to thin films; along with a decrease in the phonon frequencies as evident by Raman measurements. Surface band bending, converse piezoelectric effect, and photoelastic effects are employed to explain these behaviors. As for InGaN NWs, both In-rich and Ga-rich ternary nanowires have been synthesized by simply varying growth temperature. Morphological and structural characterizations reveal a phase-separated microstructure wherein the isovalent heteroatoms are self-aggregated, forming self assembled quantum dots (SAQDs) embedded in NWs. The SAQDs are observed to dominate the emission behavior of both In-rich and Ga-rich nanowires, which has been explained by proposing a multi-level band schema.