This volume embarks on an exploration of the processual and dynamic character of grammatical constructions in emergence, both from an `emergent' and an `emerging' perspective. `Emerging' constructions develop out of their discourse contexts.Talking of emerging constructions is compatible with a view of grammar as a stable system of rules and structures which may `emerge' (i.e., come into existence) out of a pool of previously unordered elements. `Emergent' constructions on the contrary are due to the on-line production of grammar in time. The term `emergent' emphasises the fact that a grammatical structure is always temporary and ephemeral. In both senses, grammar is modelled as a highly adaptive resource for interaction. On the basis of empirical studies on spoken English, German, Hebrew, Swedish and French, the volume addresses the following questions: How can what initially appears to be construction x end up being construction y in on-line syntax? What are the local interactional needs which such processes respond to in the process of their emergence? Does the on-line (re-)modelling of a construction concern its syntactic or semantic side - or both? And finally: Should emergent grammatical structures as they unfold in real time be seen as stages in the emerging of grammar?