The separation and sequestration of anthropogenic CO₂ is one of the most effective steps to counter global warming by curtailing the excess CO₂ levels in the atmosphere. However, to achieve the global climate change targets, in addition to the capture of CO₂ from the point sources, complementary carbon-negative technologies that capture CO₂ directly from the atmosphere are also necessary. The most crucial aspect of any CO₂ capture technology is the selection of a suitable sorbent, which is the most efficient in a specific temperature, pressure, and moisture range. The urgent nature of the CO₂ crisis has led to overwhelming contributions from researchers globally in terms of different sorbents, measurement techniques, reactors, and processes. Additionally, to develop a commercially viable CO₂ capture technology, a detailed and holistic techno-economic analysis is also vital. In this review, we have documented the recent progress on CO₂ capture studies using different solid sorbents under various operational conditions, along with the methodologies and reactors used for these studies. Furthermore, this review presents a detailed account of the industrial status of various existing CO₂ capture technologies, including direct air capture and its techno-economic prospects. This review aims to provide a bird’s eye view of the status of CO₂ capture research with a particular emphasis on the most recent developments in this field.