Cellular structures are largely found in nature such as wood, bones, cork, honeycomb etc., due to excellent properties, for example excellent energy absorption, high strength-to-weight-ratio, and lightweight. Cellular structures are made up of an interconnected network of plates (closed- cell structures), solid struts (open-cell structures) or small unit cells (periodic structures). When compared with traditional manufacturing processes, Additive Manufacturing (AM) has enabled the designers and engineers to fabricate intricate geometries having cellular structures for various applications in automotive, aerospace, biomedical, and footwear industries. All major industries have been exploiting the benefits of cellular structures due to their prevalence over a wide range of research fields. In this study, authors aim to present a comprehensive review of design, optimization, and AM of various cellular structure morphologies investigated by different researchers. In addition, the applications and properties of 3D printed structures, and the major challenges are presented. Furthermore, major gaps, limitations and new areas that needs to be investigated in cellular structures for AM area of research. This review would provide a more precise understanding and the state-of-the-art of AM with the cellular structures for engineers and researchers in both academia and industrial applications.