With recent advances in nanophotonics and nanofabrication, considerable progress has been achieved in realizations of thin composite layers designed for full absorption of incident electromagnetic radiation, from microwaves to the visible. If the layer is structured at a subwavelength scale, thin perfect absorbers are usually called ``metamaterial absorbers'', because these composite structures are designed to emulate some material responses not reachable with any natural material. We will present a general, conceptual overview of the fundamental mechanisms of full light (or microwave radiation) absorption in thin layers. Possible topologies of perfect metamaterial absorbers are classified based on their fundamental operational principles. For each of the identified classes we provide design equations and give examples of particular realizations.