The article introduces a version of von Stechow’s (1984) theory of comparatives as the most far-reaching and widely adopted foundation of semantic analyses of comparison constructions. It illustrates the range covered by this theory by applying it to other constructions like superlatives, equatives and so on. Various kinds of negation are pointed out as an area for further research. The theory serves as the starting point of two research projects that the field is currently engaged in: on the one hand, the interaction of comparison with quantification, and on the other hand, the range of crosslinguistic variation that comparison constructions are subject to. The present state of affairs is sketched for both domains.