Understanding shapes has been a challenging issue for many years, firstly motivated by computer vision and more recently by many complex applications in diverse fields, such as medical imaging, animation, or product modeling. Moreover, the results achieved so far prompted a significant amount of work in very innovative research fields such as semantic-based knowledge systems dealing with multi-dimensional media.This paper describes the historical evolvement of the research done at IMATI-GE/CNR in the field of shape understanding. The most significant methods developed are classified and described along with some results, and discussed with respect to applications. Open issues are outlined along with future research plans.