Mini and micro robots, which can swim in an underwater environment, have drawn widespread research interests because of their potential applicability to the medical or biological fields, including delivery and transportation of bio-materials and drugs, bio-sensing, and bio-surgery. This paper reviews the recent ideas and developments of these types of self-propelling devices, ranging from the millimeter scale down to the micro and even the nano scale. Specifically, this review article makes an emphasis on various propulsion principles, including methods of utilizing smart actuators, external magnetic/electric/acoustic fields, bacteria, chemical reactions, etc. In addition, we compare the propelling speed range, directional control schemes, and advantages of the above principles.