Abstract: The metasurface is an ultra-thin two-dimensional planar array that enables multi-functional and extraordinary electro-magnetic control. It consists of structural units of metamaterials which can flexibly and effectively control the phase, polarization mode and propagation mode of electromagnetic waves. Therefore, it shows great potentials and prospects in various applications including the controllable "smart" surfaces, novel waveguide structures, electromagnetic wave absorption and the miniaturized cavity resonators. In this review, we first introduce basic concepts and background of metasurfaces, and then summarize the design and development of several absorptive metasurface devices in the infrared & terahertz (THz) bands and finally discuss its potential problems and prospective in future.