Recent development in micro-fabrication technologies has enabled a variety of miniaturized fluidic system consisting of micro-ducts, valve, pumps and various injection systems. With the rapid development of microfluidics in the past few years, electroosmosis has drawn a wide attention due to its fluid controlling ability. Hence many microfluidic devices use electrokinetic flow to transport, separate and mix samples. This thesis addresses the following three topics relevant to electrokinetic phenomena in microfluidic systems: (1) numerical investigation of electroosmostic flow mixing in a converging Y-shaped micromixer with various inlet bifurcation angles; (2) depth-average electrokinetic instability model for the dilute binary electrolyte with concentration gradient; (3) steady state and dynamic aspects of electroosmotic driven flow in the open-end and close-end irregular shaped microchannels under the application of direct current (dc) and sinusoidally alternating current (ac) electric fields for micro-actuator applications.