Living organisms have evolved, over billions of years, to develop specialized biostructures with switchable adhesion for various purposes including climbing, perching, preying, sensing, and protecting. According to adhesion mechanisms, switchable adhesives can be divided into four categories: mechanically-based adhesion, liquid-mediated adhesion, physically-actuated adhesion and chemically-enhanced adhesion. Mimicking these biostructures could create smart materials with switchable adhesion, appealing for many engineering applications in robotics, sensors, advanced drug-delivery, protein separation, etc. Progress has been made in developing bioinspired materials with switchable adhesion modulated by external stimuli such as electrical signal, magnetic field, light, temperature, pH value, etc. This review will be focused on new advance in biomimetic design and synthesis of the materials and devices with switchable adhesion. The underlying mechanisms, design principles, and future directions are discussed for the development of high-performance smart surfaces with switchable adhesion.