High-performance thermoplastic polymers, such as Poly(aryl ether ketone)s (PAEK)s, can be used in various space applications due to their high mechanical properties, low density, and low outgassing properties. Polyether ether ketone (PEEK) is a thermoplastic semi-crystalline polymer belonging to the PAEKs family, which, together with its composites, has been proved to be processable via Additive Manufacturing, in particular via Fused Filament Fabrication (FFF), enabling the production of parts both on-ground and possibly even for out-of-earth. In the past years, extensive efforts have been spent on the improvement of 3D-printed polymeric structures, extending the applications of high-performance polymers from purely mechanical to functional ones. It is possible to confer new properties to polymers by mixing and blending tailored fillers and different additives (e.g., clays, NdFeB powders, magnetite, and carbon fillers). Composite and nanocomposite polymers present customized functional properties such as electrical conductivity, thermal conductivity, soft and hard magnetic properties absent or utterly different from the ones of pure polymer. In this paper, we report the state of the art on 3D-printed PEEK composites, their mechanical properties, and functionalities in view of the production of parts made of PEEK composites and nanocomposites, and their possible space applications (e.g., electromagnetic devices, magnetic shielding, thermal protection system and sensors).