Nanorods, nanowires, and nanotubes of ferroelectric perovskites have recently been studied with increasing intensity due to their potential use in non-volatile ferroelectric random access memory, nano-electromechanical systems, energy-harvesting devices, advanced sensors, and in photocatalysis. This Review summarizes the current status of these 1D nanostructures and gives a critical overview of synthesis routes with emphasis on chemical methods. The ferroelectric and piezoelectric properties of the 1D nanostructures are discussed and possible applications are highlighted. Finally, prospects for future research within this field are outlined.