The development of a light emitter compatible with Si based complementary metal-oxide- semiconductor (CMOS) circuit technology and fast optical interconnects is important for the new generations of microprocessors and computers. Self-assembled Si/Si_1-xGe_x nanostructures (NSs) with light emission in the important optical communication wavelength of 1.3 – 1.55 μm are compatible with conventional CMOS processes. However, the predicted and experimentally confirmed long carrier radiative lifetimes in Si and Si/Si_1-xGe_x NSs impede the demonstration of efficient light-emitting devices and lasers. Thus, engineering of Si/Si_1-xGe_x heterostructures with controlled composition and interface abruptness is critical in producing the desired fast and efficient photoluminescence (PL) peaked around 0.8-0.9 eV. In this paper we assess how the nature of the interfaces between SiGe NSs and Si in heterostructures strongly affects carrier mobility and recombination for physical confinement in one dimension (corresponding to the case of quantum wells), two dimensions (quantum wires), and three dimensions (quantum dots). The interface sharpness is influenced by many factors such as growth conditions, strain, and thermal processing, which in practice can make it difficult to attain the ideal structures required. This is certainly the case for NS confinement in one dimension. However, we demonstrate that axial Si/Ge nanowire (NW) heterojunctions (HJs) with a Si/Ge NW diameter in the range 50 – 120 nm produce a clear PL signal associated with band-to-band electron-hole recombination at the NW HJ that is attributed to a specific interfacial SiGe alloy composition. For three-dimensional confinement, the experiments outlined here show that two quite different Si_1-xGe_x NSs incorporated into a Si_0.6Ge_0.4 wavy structure exhibit an intense PL signal with a characteristic decay time as much as 1000 times shorter than that observed in conventional Si/SiGe NSs. The experimentally observed non-exponential PL decay in Si/SiGe NSs is explained as being due to variations of the distances separating electrons and holes at the Si/SiGe heterointerface. The results demonstrate that an abrupt Si/SiGe heterointerface reduces the carrier radiative recombination lifetime and increases the PL quantum efficiency making these SiGe NSs promising candidates for applications in CMOS compatible light-emitting devices.