As the introductory paper of a collection of articles, this contribution has a threefold purpose. First, it briefly outlines the major developments of research in grammaticalization during the last decades, the most promising of which can be found in approaches combining grammaticalization with language comparison, diachronic reconstruction, and linguistic variation, and in models taking into account the role of contexts and constructions in grammaticalization processes. Second, this contribution lists problems and areas of dispute that have arisen inside the framework, and criticism that has been put forward from outside. Naturally, the main intention of this section cannot be to come up with final solutions to any of these questions; instead it suggests an evaluation of the scope, relevance and justification of single items of the debate. The third part summarizes the six papers presented in this volume, highlighting connections and points of convergence between them, and pointing out their relevance to the open questions mentioned before.