Herein the recent experiments performed by the authors on fabricated multi-walled BN nanotubes and monoatomic BN graphene-like nanosheets are reviewed. The results are presented in several sections, namely: (i) method for high-yield synthesis of thin, defect-free BN nanotubes of only a few-layers, with external diameters below 10 nm; (ii) verification of BN nanotube piezoelectrical behavior and its electrically-induced thermal decomposition under combined resistive heating and electrical charging in a transmission electron microscope; (iii) the first direct measurements of the true tensile strength and Young’s modulus of BN nanotubes, using newly developed nanotensile tests inside an electron microscope; the measured values were found to be ∼30 GPa and ∼900 GPa, respectively; and (iv) diverse kinetic processes taking place within the prepared monoatomic BN sheets (so-called “white graphenes”) affiliated with intensive knock-on B and N atom displacements under high energy electron beam irradiation in an aberration-corrected medium-voltage high-resolution transmission electron microscope.