Abstract This paper documents and reviews the state of the art concerning computational models of construction grammar learning. It brings together prior work on the computational learning of form-meaning pairings, which has so far been studied in several distinct areas of research. The goal of this paper is threefold. First of all, it aims to synthesise the variety of methodologies that have been proposed to date and the results that have been obtained. Second, it aims to identify those parts of the challenge that have been successfully tackled and reveal those that require further research. Finally, it aims to provide a roadmap which can help to boost and streamline future research efforts on the computational learning of large-scale, usage-based construction grammars.