mixing is of uttermost importance in bio- and chemical analyses using micro TAS (total analysis systems) or lab-on-chips. Many microfluidic applications involve chemical reactions where, most often, the fluid diffusivity is very low so that without the help of chaotic advection the reaction time can be extremely long. In this article, we will review various kinds of mixers developed for use in microfluidic devices. Our review starts by defining the terminology necessary to understand the fundamental concept of mixing and by introducing quantities for evaluating the mixing performance, such as mixing index and residence time. In particular, we will review the concept of chaotic advection and the mathematical terms, Poincare section and Lyapunov exponent. Since these concepts are developed from nonlinear dynamical systems, they should play important roles in devising microfluidic devices with enhanced mixing performance. Following, we review the various designs of mixers that are employed in applications. We will classify the designs in terms of the driving forces, including mechanical, electrical and magnetic forces, used to control fluid flow upon mixing. The advantages and disadvantages of each design will also be addressed. Finally, we will briefly touch on the expected future development regarding mixer design and related issues for the further enhancement of mixing performance.