Metamaterials are a kind of artificial material with special properties, showing huge potential for applications in fields such as infrared measurement, solar cells, optical sensors, and optical stealth. A metamaterial perfect absorber (MPA) is designed based on a metamaterial, featuring strong absorption, small volume, light weight, ultra-bandwidth, tunability and other characteristics. This paper introduces the absorption mechanism of MPAs from microwave to optical wave band, and four directions of absorber design are elaborated. Equivalent impedance matching, plasma resonance and interference effect are the main absorption mechanisms of MPA. Multiband perfect absorption, ultra-wideband and ultra-narrowband perfect absorption, polarization and angle insensitive absorption, and dynamically controllable tunable absorption are the main design aspects. Among them, the proposal of a dynamically tunable absorber realizes the dynamic absorption. Finally, the problems and challenges of metamaterial perfect absorber design are discussed.