Acid gas removal from gaseous streams such as flue gas, natural gas and biogas is mainly performed by chemical absorption with amines, but the process is highly energy intensive and can generate emissions of harmful compounds to the atmosphere. Considering the emerging interest in carbon capture, mainly associated with increasing environmental concerns, there is much current effort to develop innovative solvents able to lower the energy and environmental impact of the acid gas removal processes. To be competitive, the new blends must show a CO2 uptake capacity comparable to the one of the traditional MEA benchmark solution. In this work, a review of the state of the art of attractive solvents alternative to the traditional MEA amine blend for acid gas removal is presented. These novel solvents are classified into three main classes: biphasic blends—involving the formation of two liquid phases, water-lean solvents and green solvents. For each solvent, the peculiar features, the level of technological development and the main expected pros and cons are discussed. At the end, a summary on the most promising perspectives and on the major limitations is provided.