Lab-on-a-chip is an enabling technology that has influenced areas from biology, drug research to the development of point-of-care devices. The essential of Lab-on-a-chip technology is the "mobile liquid" in channels with dimensions of tens to hundreds of micrometres, for which a liquid pumping system generally is indispensable. We review the methods for pumping fluids on biomedical lab-on-a-chip developed over the last decade with the emphasis on their basic principles and typical applications. Electroosmosis and pressure are the two methods most widely employed. Pressure can be generated by various means, including positive displacement, reciprocating displacement, gravity, surface tension, centrifuging, etc. In the discussions of these techniques, we provide a number of important biomedical applications in an effort to show the potential of microfluidics for those outside this field who can potentially benefit from this technology.