Kinematics plays a crucial role in additive manufacturing (AM), including the synergic movements and relative positioning of different machine components to create the final three-dimensional (3D) model. Therefore, it is essential to understand the underlying kinematics of the machine set-up in use to produce high-quality prints, including complex geometries, intricate shapes, and difficult-to-reach overhangs and underlying supports. Achieving the desired efficiency and required accuracy while printing significantly measures the machine’s capabilities and kinematic limits. The overall machine kinematics includes not only the coordinated movements of the print head and the build platform but also the material feeding and curing mechanisms. Factors such as the machine type, material choice and form, and the desired resolution of the printed part also contribute to the overall kinematic requirements. The kinematic analysis of an AM machine system also includes the properties of printer components, motion control algorithms, and the software used for process control. In this research, various state-of-the-art AM set-ups have been described with dedicated applications for metals (multi-station multi-axis hybrid layered manufacturing (MSMA-HLM), electron beam hybrid manufacturing (EBHM)), thermoplastics (plastic additive manufacturing (PAM), foam additive manufacturing (FAM)), ceramics (sand 3D printing (Sand-3DP)), composites (optimal laminated additive manufacturing (Opti-LAM)), and jettable liquids (sub-zero additive manufacturing (SAM)). Fabricated sample parts are also described. Investigating the various kinematic set-ups can help in enhancing the capabilities and efficiency of additive manufacturing techniques, leading to advancements in the field of rapid manufacturing.