Additive manufacturing is a very rapidly developing industrial field. It opens many possibilities for the fast fabrication of complex-shaped products and devices, including functional materials and smart structures. This paper presents an overview of polymer 3D printing technologies currently used to produce magnetic materials and devices based on them. Technologies such as filament-fused modeling (FDM), direct ink writing (DIW), stereolithography (SLA), and binder jetting (BJ) are discussed. Their technological features, such as the optimal concentration of the filler, the shape and size of the filler particles, printing modes, etc., are considered to obtain bulk products with a high degree of detail and with a high level of magnetic properties. The polymer 3D technologies are compared with conventional technologies for manufacturing polymer-bonded magnets and with metal 3D technologies. This paper shows prospective areas of application of 3D polymer technologies for fabricating the magnetic elements of complex shapes, such as shim elements with an optimized shape and topology; advanced transformer cores; sensors; and, in particular, the fabrication of soft robots with a fast response to magnetic stimuli and composites based on smart fillers.