The development of new, efficient and cost-effective technologies for acid gases (CO2 and H2S) removal from natural gas is pertinent for cleaner energy productions. The removal of acid gases from natural gas can be carried out using different techniques (chemical, physical or hybrid). Although the widely employed techniques are generally effective, they have some ascribed drawbacks such as process efficiency and high-energy cost. Emerging techniques are being considered to reduce or eliminate these limitations but their deployment on an industrial scale may require that certain scientific and technological criteria, such as higher selectivity and gas separation kinetics, be met. Unprecedented and lacking in previous appraisals, this review has focused on the emerging and sustainable developments on acid gases removal from natural gas, but not without a critical evaluation of the existing technologies to provide a better background on the subject, ascertain the status-quo and identify gaps for further improvements. Efficiency of these emerging technologies are analysed with focus on ionic liquids and their blends, binding organic liquids, enzyme-based separation technologies and others. This review also features the brief contribution of the authors towards the development of low-cost materials for CO2/natural gas separation. This article is expected to serve as an in-depth requisite background for further research on carbon capture processes with respect to natural gas purification.