Currently, additive manufacturing (AM) technology has received significant attention from both academia and industry. AM is characterized by fabricating geometrically complex components in a layer-by-layer manner, and greatly reduces the geometric complexity restrictions compared with traditional manufacturing. As AM is no longer limited to the normal three degrees of freedom (DOF) (three-axis) systems, there are many new multi-DOF AM machines been developed with various aims. It is, therefore, necessary that a review of the topic with regard to multi-DOF AM is performed for future AM system development. This paper, focuses on reviewing publications related to multi-DOF AM according to the number of DOF on an AM machine. The major part of the paper aims to inspire both researchers and engineers to further develop and improve multi-DOF AM systems to achieve different goals. The final part of the paper discusses the findings together with future research directions.