Indium nitride (InN), because of its recently discovered narrow band-gap and superior electron transport properties, has emerged as a potentially important semiconductor for use in near-infrared (NIR) optoelectronics, solar cells, and high-speed electronics. The current barrier for extensive fundamental studies and widespread applications of InN is mostly related to the growth difficulty of high-quality InN heteroepitaxial films. We have recently demonstrated that high-quality InN/AlN heterostructures can be formed on Si(111) due to the existence of "magic" ratios between the lattice constants of comprising material pairs: 2:1 (Si:Si3N4), 5:4 (AlN/Si), and 8:9 (InN:AlN). This new route of lattice matching allows the formation of commensurate interface with a common two-dimensional superlattice. For InN growth on AlN with nitrogen polarity, we found that the pseudomorphic to commensurate lattice transition occurs within the first monolayer of growth, resulting in an abrupt heterojunction at the atomic scale. At room temperature, the as-grown InN films on Si exhibit strong NIR photoluminescence with the peak energy at ~0.65 eV (wavelength at ~1.9 μm). Combined with the optical absorption measurements performed by transmission and spectroscopic ellipsometry, we confirmed that InN is a direct narrow band-gap semiconductor. Therefore, InN is a very ideal material for applications in NIR optoelectronics and solar cells, if other technological barriers (e.g., p-type doping) can also be overcome. In addition to the measurements of fundamental optical properties, a large valence band offset (3.10 eV) of type-I band alignment was also determined by photoelectron spectroscopy for the InN/AlN 8:9 commensurate heterojunction. The large band offsets and the strong polarization effects make the InN/AlN heterostructures very promising for applications in heterojunction field-effect transistors.