This article presents numerous state-of-the-art metamaterial-based microwave absorber applications of negative permittivity, negative permeability and zero reflectivity materials. Discussion begins with basic narrow band, multiband and wide band absorbers. The discussion that follows describes sophisticated 3D design approaches for absorbers based on rigorous permittivity and permeability analysis and equivalent circuit modeling to explain the absorber characteristics and predict performance. Practical applications include RF energy harvesting, sensors, antennas, radar cross-section reduction, EMI/EM compatibility, polarization conversion and many others, and applications at terahertz and optical frequencies in addition to microwave are briefly mention.