Carrying out similarity and analogy comparisons can be modeled as the align
ment and mapping of structured representations. In this article we focus on
three aspects of comparison that are central in structure-mapping theory.
All three are controversial. First, comparison involves structured represen
tations. Second, the comparison process is driven by a preference for conne
cted relational structure. Third, the mapping between domains is rooted in
semantic similarity between the relations that characterize the domains. Fo
r each of these points, we review supporting evidence and discuss some chal
lenges raised by other researchers. We end with a discussion of the role of
structure mapping in other cognitive processes.