Locomotion at micro and nano scales is a challenge and has drawn attention for over six decades. Inspired by nature, studies have mimicked nanoswimming organisms, which use rotating or beating flagella for locomotion. This mode of propulsion, also known as flagellar propulsion, has been explored extensively in the literature. However, chemical and magnetic methods have gained interest in the last decade owing to advantages including high thrust force and wireless control. The review summarizes chronologically the various propulsion mechanisms for moving a nanoswimmer using chemical fuel, magnetic fields, ultrasonic pulses and thrust force generated by bacteria in the presence of external stimuli including laser light, and thermal and chemical gradients.