Indium nitride (InN) is an interesting and potentially important semiconductor material with superior electronic transport properties. Compared to all other group III-nitrides, InN possesses the lowest effective mass, the highest mobility, the highest saturation velocity and narrow band gap of 0.7-0.9 eV. The present paper deals with the fabrication of InN nanostructures on silicon and sapphire substrates by plasma-assisted molecular beam epitaxy. The droplet epitaxy and Stranski-Krastanov(S-K) growth modes were used to grow the nanostructures. © 2011 American Institute of Physics.