This short paper is mainly the introduction oJ the a~ailable INRIA Research Report No. 2050 (55 page,) published by the author in Sept. 1993 . The automated analysis of 3D medical images can improve significantly both diagnosis and therapy. This automation raises a number of new fascinating research problems in the fields of computer vision and robotics. In this paper, I propose a list of such problems after a review of the current major 3D imaging modalities, and a description of the related medical needs. I then present some of past and current work done in the research group EPIDAURE ] at INRIA, on the following topics: segmentation of 3D images, 3D shape modeling, 3D rigid and nonrigid registration, 3D motion analysis and 3D simulation of therapy. I also try to suggest a number of promising research tracks and future challenges.