InSb nanostructures embedded in InAs and InAsSb matrices were grown on InAs (001) and GaAs (001) substrates by molecular beam epitaxy. The diameter and height of InSb quantum dots (QDs) on InAs with 2ML-InSb coverage grown by Stranski-Krastanov (S-K) are ∼36.8 nm and ∼3.1 nm, respectively. The density of QDs is ∼2.5×10 10 cm -2. The size distribution of InSb QDs on InAs with 2ML-InSb coverage grown by migration enhanced epitaxy (MEE) was larger than that of its S-K counterpart. Unique InSb quantum dashes (Q-dashes) on InAsSb elongated along two directions were found on an AlSb-buffered GaAs substrate. InSb Q-dashes grown by migration enhanced epitaxy (MEE) were ∼159 nm in length, ∼63 nm in width, and ∼11 nm in height. A large reduction of volume of InSb structures between those in the matrix and those on the surface was found. Threading disl°Cations resulting from the Q-dash structures were also observed. This may be attributed to As-Sb exchange.