Continuous laser vaporization of a BN target under N2 atmosphere is up to now the unique route to single-walled boron nitride nanotubes (BN-SWNTs). Although grams of product can be obtained by this technique, the raw material contains in addition to the BN-SWNTs, different by-products made of boron and nitrogen. Since these materials are undesirable for the studying of the intrinsic properties of the nanotubes, we have undertaken a purification process using chemical and physical methods to separate the different components. We show here that most impurities can be removed by successive cycles of washing, sonication, and centrifugation. Furthermore, the two different types of boron nitride nanostructures i.e., BN-SWNTs and BN-cages can be isolated. Efficiency of the separation was monitored by transmission electron microscopy (TEM) at the different steps of the process. Finally, we envisage the further purification of the nanotubes-enriched fraction by functionalizing the nanotubes in a non covalent manner by specific polymers as for carbon nanotubes and BN multi-walled nanotubes.