Different electrically-thin absorbing designs based on High-Impedance Surfaces (HIS) are presented and classified on the basis of the nature of loss. HIS structures allow achieving absorption by exploiting either dielectric or ohmic (resistive) losses. The former ultra-narrowband absorption phenomenon can be obtained by employing dielectric losses of commercial substrates. The resonant structure, often referred to as Perfect Metamaterial Absorber, usually comprises a metallic frequency selective surfaces located above a ultra-thin grounded dielectric substrate. The metamaterial absorber is also angularly stable because of its reduced thickness. Alternatively, if a loss component is introduced in the frequency selective surface located in front of the grounded dielectric substrate both narrowband and wideband absorbing structures can be designed.