A lab-on-a-chip device typically integrates many microfluidic components and has similar functions to the room-sized laboratory. However, developing such a lab-on-a-chip device is not simply to scale down the conventional instruments. It requires the understanding and controlling of many multiscale physical and chemical phenomena, spanning from centimeter to nanometer. In this paper, we provide an overview of the multiscale fluidic phenomena encountered in lab-on-a-chip devices, with focus on electrokinetics. We review different computational models for the studies of microfluidics and nanofluidics. Several application examples using microfluidics and nanofluidics, including micromixing, particle/cell separation, and DNA separation, are given. (c) 2007 Elsevier Ltd. All rights reserved.