Cognitive linguistics has reached a stage of maturity where many researchers are looking for an explicit formal grounding of their work. Unfortunately, most current models of deep language processing incorporate assumptions from generative grammar that are at odds with the cognitive movement in linguistics. This demonstration shows how Fluid Construction Grammar (FCG), a fully operational and bidirectional unification-based grammar formalism, caters for this increasing demand. FCG features many of the tools that were pioneered in computational linguistics in the 70s-90s, but combines them in an innovative way. This demonstration highlights the main differences between FCG and related formalisms.