Recent years have seen considerable progress in the development of microfabricated systems for use in the chemical and biological sciences. The term micro total analytical system (µTAS) is now a well-accepted concept. Much development has been driven by a need to perform effective manipulation of chemical and biological liquids with small volumes at micro and/or nano flowrate level in these systems. In this review, the focus will be on the pumping techniques used for delivery and control of liquids, especially those physical-chemical 'continuous dynamic flow micropumps'. The principles of these pumping techniques are mainly based on one or several well-known phenomena such as electrical, light, magnetic, thermal and other actuated mechanisms. Electrokinetically-driven continuous flow pumps such as the electrophoretic pump and electroosmotic pump, surface chemistry based continuous flow micropumps such as the opto-electrowetting-based pump, optically-driven pump, electrochemical pump and constant gravity-driven pump, and combination-driven techniques such as hydrodynamic flow and electrokinetic/gravity/magnetophoretic pumping will be summarized. The focus will be on the research highlights, trends and future of these pump techniques. Finally, mixing techniques on the microscale are briefly reviewed.