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Cellular structures (CSs) have been used extensively in recent years, as they offer a unique range of design freedoms. They can be deployed to create parts that can be lightweight by introducing controlled porous features, while still retaining or improving their mechanical, thermal, or even vibrational properties. Recent advancements in additive manufacturing (AM) technologies have helped to increase the feasibility and adoption of cellular structures. The layer-by-layer manufacturing approach offered by AM is ideal for fabricating CSs, with the cost of such parts being largely independent of complexity. There is a growing body of literature concerning CSs made via AM; this presents an opportunity to review the state-of-the-art in this domain and to showcase opportunities in design and manufacturing. This review will propose a novel way of classifying cellular structures by isolating their Geometrical Degrees of Freedom (GDoFs) and will explore the recent innovations in additively manufactured CSs. Based on the present work, the design inputs that are common in CSs generation will be highlighted. Furthermore, the work explores examples of how design inputs have been used to drive the design domain through various case studies. Finally, the review will highlight the manufacturability limitations of CSs in AM.