Nonconventional or advanced machining processes such as electric discharge machining, electrochemical machining, abrasive water jet machining, and laser beam machining have been widely used as a viable alternate to the conventional processes to manufacture high-quality engineered parts having certain typical features. In spite of their special features, wider acceptance, and use, they suffer from certain inherent limitations with regard to sustainability such as high consumption of energy and resources; generation of toxic liquid, gases, and solid wastes; risk for health and safety; air pollution; generation of waste and its disposal problems; and workpiece contamination and thermal damage to the parts being produced. It is found that these factors all adversely affect the environment to a certain extent. Innovative sustainable techniques such as dry, near-dry, and green electric discharge machining; green and hybrid electrochemical machining; ice-jet machining; and eco- and underwater laser beam machining, etc. have been developed to address sustainability challenges and greatly benefited with improvements in quality, productivity, and sustainability. This review article first introduces four major nonconventional machining processes, discusses their inherent sustainability issues and challenges, and presents state-of-the-art review of the work conducted using sustainable innovative techniques and strategies with an aim to encourage academics, researchers, and engineers for research and developments in order to establish the field further. The literature review offered in this article is based on over 80 articles published from 1975 to 2017. Finally, the article ends up with concluding remarks and recommending possible avenues to stimulate future research.