This paper presents the development of extrusion-based additive manufacturing (AM) processes of short carbon fiber-reinforced thermoplastic composites for the creation of relatively large aerospace structures. One of the custom-made AM infrastructures used is composed of a six-axis robotic arm with a maximum reach of 1.8 m enabling large printing envelope, a heated printing bed and a heating enclosure. Both heating systems are required for the printing of high-temperature resistance thermoplastics and their composites. To increase the process productivity, different high-flow extrusion-based printheads are used, allowing much higher throughputs, typically by two orders of magnitude compared to desktop-sized Fused Filament Fabrication (FFF) systems. The AM platform has been successfully used for our various projects with aerospace industry to manufacture technological demonstrators. The two main examples are (i) non-planar multi-layer acoustic components for efficient sound absorption of aircraft engines, and (ii) for some structural components of a composite lunar rover. Our current efforts are on improving the AM processes to achieve higher productivity while providing the required mechanical properties.