Piezoelectric nanostructures, including nanofibers, nanotubes, nanojunctions and nanotrees, may be made of piezoelectric materials alone, or as composites of piezoelectric materials and electrically-conductive materials. Homogeneous or composite nanofibers and nanotubes may be fabricated by electrospinning. Homogeneous or composite nanotubes, nanojunctions and nanotrees may be fabricated by template-assisted processes in which colloidal suspensions and/or modified sol-gels of the desired materials are deposited sequentially into the pores of a template. The electrospinning or template-assisted fabrication methods may employ a modified sol-gel process for obtaining a perovskite phase in the piezoelectric material at a low annealing temperature.