Fluid Construction Grammar (FCG) is a computational framework that provides a formalism for representing construction grammars and a processing engine that supports construction-based language comprehension and production. FCG is conceived as a computational operationalisation of the basic tenets of construction grammar. It thereby aims to establish more solid foundations for constructionist theories of language, while expanding their application potential in the fields of artificial intelligence and natural language understanding. This paper aims to provide a brief introduction to the FCG research programme, reflecting on what has been achieved so far and identifying key challenges for the future.