Microfluidic continuous cell separation based on hydrodynamic interaction in a microfluidic channel has attracted attention because of its robustness, high throughput and cell viability. This paper systematically gives an overview on recent advances in hydrodynamic particle and cell separation in microfluidic devices. It presents the basic ideas and fluid mechanics for the hydrodynamic interaction of a particle in a microfluidic system. Secondly, different kinds of devices are introduced with detailed descriptions of their mechanisms, designs and performances. Finally, the review addresses some practical issues of microfluidic sorting devices for use in biological or medical studies.