Additive Manufacturing (AM) techniques have recently attracted the attention of scientists for the development of prototypes with complex or particular geometry in a fast and cheap way. Among the different AM processes, the Fused Deposition Modelling process (FDM) offers several advantages in terms of costs, implementation features and design freedom. Recently, it has been adopted to realise auxetic structures, which are characterised by negative Poisson ratio, enhanced mechanical properties, and a higher compression resistance than conventional structures. This review outlines the use of AM processes, in particular FDM, to design and obtain auxetic structures, with the final aim to exploit their applications in different fields. The first part of this work presents a brief classification of auxetic structures and materials. Subsequently, a summary of additive manufacturing processes is presented, focusing on the use of FDM and its limitations. Finally, the studies on the use of additive manufacturing to produce auxetic structures are shown, evidencing the potential of the concurrent combination of a fast prototyping technique such as FDM and the characteristics of polymer- and/or composite-based auxetic structures. Indeed, this new technological field opens the possibility of realising novel structures with integrated smart behaviour, multifunctional properties, compression resistance, and a tailored microstructure and shape.