Epitaxially-grown three-dimensional Si/SiGe nanostructures (NSs) produce photoluminescence (PL) and electroluminescence in the desired spectral range of 1.3-1.6 μm. We show that by controlling and modifying such Ge-rich SiGe nanoclusters during growth it is possible to fabricate very fast (PL lifetime <20 ns) and hence more efficient SiGe light-emitting devices. The results presented here demonstrate that in such Si/SiGe 3D NSs with a nominal Ge concentration approaching ∼35% the PL peaked near 0.78 eV strongly depends on the Si/SiGe heterointerface abruptness. In other Si/SiGe NS/quantum-well samples with a Ge concentration approaching ∼40%, we find two PL bands peaked at ∼0.8 eV and ∼0.9 eV at low temperatures. The PL peaked at 0.8 eV rises and decays slowly, and it quickly saturates as the excitation intensity increases. In contrast, the PL peaked at 0.9 eV shows a much shorter lifetime and exhibits a linear dependence versus excitation intensity. The slow/delayed PL at 0.8 eV is attributed to carrier recombination at the SiGe NS/Si transition layer while the faster and more efficient PL at 0.9 eV is associated with SiGe quantum wells. More complicated and similarly fast (∼10-7 s) decays are observed at very high excitation intensities due to electron-hole droplet formation. The physics of carrier recombination in these Si/SiGe NSs is discussed.