Idiosyncrasy is an important property of the language that enables it to be productive and at the same time prevents it from growing infinitely large. Idiosyncrasymeans having a peculiar statistical, semantic or syntactic behavior. Idiosyncratic phrases are commonly referred to as Multiword Expressions (MWEs) and have application in most natural language processing (NLP) tasks. The ability to identify and generate MWEs is essential for an NLP system designed to interact in and understand human language. Presently,most models of identifying idiosyncrasy suffer from a low precision. In order to improve the quality of MWE-related systems, more formal definitions of idiosyncrasy as well as more complex computational models need to be developed. This work attempts to define idiosyncrasy on statistical and distributional grounds and study it froma computational perspective. It also presents various models for identifying different types ofMWEs with a focus on nominal MWEs.