In comparison to the conventional manufacture of curved profiles by bending, the curved profile extrusion (CPE) offers advantages concerning a flexible, precise, and cost effective production especially in small quantities. A relatively new development is the enhancement of CPE for the manufacture of three-dimensionally curved profiles for which additional parameters like gravity and thermal constraints have to be taken into account to obtain an accurate result. One part of the investigations is quenching, which is necessary to achieve the material properties according to the grain structure, but also for the prevention of an undesired warm bending effect, which occurs due to the gravity influence superimposed on the curved profile extrusion. In connection with the manufacture of small radii the torsion effect acts additionally on the deflected profile and degrades the contour accuracy. To prevent the torsion and bending effects as far as possible, the application of a robot with a specific supporting strategy is necessary. This paper describes the current state of extensive basic research at the Institute of Forming Technology and Lightweight Construction (IUL) concerning the production of three-dimensionally curved profiles.