The current status of research on boron-carbon-nitrogen (B-C-N) and boron nitride (BN) nanotubes is presented. The latest achievements in syntheses, analyses and property measurements of these nanoscale tubular architectures are reviewed. The characteristic features of B-C-N and BN nanotubes, compared with conventional C nanotubes, are paid special attention. In particular, the latest breakthroughs in the chemical vapour deposition synthesis of BN nanotubes and an insight into their unique structures are highlighted. A wide range of potential applications is also envisaged, based on the recent progress, which includes pioneering results in BN nanocable fabrication, gas adsorption, electron transport and field emission measurements.