The present study deals with phraseological units (PUs), i.e. conventionalized realtively stable multiword items of a given language exhibiting various kinds of irregularities in their structure. It demonstrates what difficulties their structure and variation raises for linguistic theory and offers an alternative way, in which these items can be approached within the framework of Conceptual Semantics and the Tiernet model. The book addresses i.a. the problems of literal vs. idiomatic meaning, analyzability and base form of PUs. PU variants are described in terms of a connectionist network moden called construction family. A systematic formalized description of PUs is developed on the basis of a usage-based stury of the Finnish PU heittää helmiä sioille 'throw pearls to pigs'.