Metasurfaces are ultrathin metamaterials constructed by planar meta-atoms with tailored electromagnetic responses. They have attracted tremendous attention owing to their ability to freely control the propagation of electromagnetic waves. With active elements incorporated into metasurface designs, one can realize tunable and reconfigurable metadevices with functionalities controlled by external stimuli, opening up a new platform to dynamically manipulate electromagnetic waves. In this article, we review the recent progress on tunable and reconfigurable metasurfaces, focusing on their operation principles and practical applications. We describe the approaches to the engineering of reconfigurable metasurfaces categorized into different classes based on the available active materials or elements, which can offer uniform manipulations of electromagnetic waves. We further summarize the recent achievements on programmable metasurfaces with constitutional meta-atoms locally tuned by external stimuli, which can dynamically control the wavefronts of electromagnetic waves. Finally, we discuss time-modulated metasurfaces, which are meaningful to exploit the temporal dimension by applying a dynamic switching of the coding sequence. The review is concluded by our outlook on possible future directions and existing challenges in this fast developing field.