Additive Manufacturing (AM), also known as a three-dimensional (3D) printing, is one of the disruptive technologies in the manufacturing industry that can change current production systems into more sustainable ones. In contrast to the older manufacturing processes, both subtractive and formative, AM produces components by printing layers on top of each other, neither reducing raw material wastage nor deterioration, expands the options of design, and creates products in tiny amounts and on-demand manufacturing. These attributes qualify AM as a central facilitator of the sustainable production systems in accordance with the global goals of resource efficiency, reduction of carbon emissions, and implementation of the circular economy. This in-depth review critically looks at the application of additive manufacturing in sustainable production systems with a synthesis of existing literature on the sustainability aspects at environmental, economic, and social level. The paper covers key AM technologies, assesses benefits of sustainability using life cycle perspectives, lists the key challenges and limitations, and presents industrial uses and research perspectives in the future. The above findings indicate that although AM does provide significant sustainability benefits, it can only be used to full capacity with the development of new technology, standardized assessments systems, and integration of industries on the strategic level.