Electromagnetic wave absorbers have been investigated for many years with the aim of achieving high absorbance and tunability of both the absorption wavelength and the operation mode by geometrical control, small and thin absorber volume, and simple fabrication. There is particular interest in metal-insulator-metal-based plasmonic metamaterial absorbers (MIM-PMAs) due to their complete fulfillment of these demands. MIM-PMAs consist of top periodic micropatches, a middle dielectric layer, and a bottom reflector layer to generate strong localized surface plasmon resonance at absorption wavelengths. In particular, in the visible and infrared (IR) wavelength regions, a wide range of applications is expected, such as solar cells, refractive index sensors, optical camouflage, cloaking, optical switches, color pixels, thermal IR sensors, IR microscopy and gas sensing. The promising properties of MIM-PMAs are attributed to the simple plasmonic resonance localized at the top micropatch resonators formed by the MIMs. Here, various types of MIM-PMAs are reviewed in terms of their historical background, basic physics, operation mode design, and future challenges to clarify their underlying basic design principles and introduce various applications. The principles presented in this review paper can be applied to other wavelength regions such as the ultraviolet, terahertz, and microwave regions.