This work is aimed at establishing a common frame and understanding of function modeling (FM) for our ongoing research activities. A comparative review of the literature is performed to grasp the various FM approaches with their commonalities and differences. The relations of FM with the research fields of artificial intelligence, design theory, and maintenance are discussed. In this discussion the goals are to highlight the features of various classical approaches in relation to FM, to delineate what FM introduces to these fields, and to discuss the applicability of various FM approaches in these fields. Finally, the basic ideas underlying our projects are introduced with reference to the general framework of FM.