This article presents a rigorous, comprehensive review of metasurface absorbers that incorporates advancements in material science and fabrication technologies that enable optically transparent thin resistive films, reconfigurable designs, and flexible and conformal absorbers. This review systematically steps through absorber evaluation, design, fabrication and validation. Evaluation topics include broadband and selective absorbers. Design topics include multiresonance and semianylitical techniques and machine learning approaches. An overview of material selection and application-oriented considerations, experimental validation methods and data processing techniques support a discussion of manufacturability and numerous practical considerations.