Carbon dioxide capture and mitigation form a key part of the technological response to combat climate change and reduce CO2 emissions. Solid materials capable of reversibly absorbing CO2 have been the focus of intense research for the past two decades, with promising stability and low energy costs to implement and operate compared to the more widely used liquid amines. In this review, we explore the fundamental aspects underpinning solid CO2 sorbents based on alkali and alkaline earth metal oxides operating at medium to high temperature: how their structure, chemical composition, and morphology impact their performance and long-term use. Various optimization strategies are outlined to improve upon the most promising materials, and we combine recent advances across disparate scientific disciplines, including materials discovery, synthesis, and in situ characterization, to present a coherent understanding of the mechanisms of CO2 absorption both at surfaces and within solid materials.