Electromagnetic absorbing technology can effectively suppress the radiation of electromagnetic waves, and has been widely used in military and civilian fields. However, traditional absorbing technology cannot meet the new requirements for modern absorbing materials. The advent of metamaterials provides a solution for this problem Metamaterial absorber has the advantages of simple structure, light weight, high absorption rate, and can realize the flexible control of electromagnetic waves, which has led the electromagnetic absorption research to rapidly develop. In this paper, the research and development of using metamaterials to absorb electromagnetic wave is reviewed. Firstly, the principle, implementation, and presently existing bottlenecks of electromagnetic wave absorption in using metamaterials are outlined. Secondly, recent progress of the aforementioned key issues in three aspects is introduced, including multi-band and broadband, polarization and angle independence, and dynamic tunability. Several typical methods of making metamaterial absorbers are illustrated here. Generally speaking, the prerequisite of broadband metamaterial absorbers is to provide multiple resonances that are close enough to each other. The structure with multiple rotationally symmetric geometry is helpful in achieving polarization- and angle-insensitive properties. The flexible control of absorption performance can be realized by introducing lumped elements such as resistances, capacitances, and diodes. In addition, by means of composite traditional materials or new materials and other methods the dynamic adjustment of the absorption performance can be achieved. Although researchers have done a lot of work on the metamaterial absorbers, there remain many problems and challenges. For the future design, several promising directions are suggested from three perspectives: high performance, multifunctionality, and new structures. In terms of high performance, it is still a challenge to achieve ultra-thin broadband metamaterial absorber for low-frequency which can break through the limitation of wavelength. Integrated multifunctional metamaterials can adapt to the increasingly complex application scenarios and should gradually become the focus of attention. Since three-dimensional (3D) printing technology has proved to be applicable to the preparation of complex metamaterial structures, the new 3D metamerial absorbers will bring more vitality to the development of metamaterials. Finally, as regards the application of metamaterials in stealth, the future development of metamaterial absorbers is further summarized.