Invasion science is a very active subdiscipline of ecology. However, some scientists contend that theoretical integration has been limited and that predictive power remains weak. This paper, focusing on plants, proposes a new multi-pronged research strategy that builds on recent advances in invasion science. More intensive studies on particular model organisms and ecosystems are needed to improve our understanding of the full suite of interacting factors that influence invasions (‘model system research’). At the same time, comparative studies across many study systems are essential for unravelling the context-dependencies of insights that emerge from particular studies (‘multi-site studies’); and quantitative synthesis based on large datasets should be constrained to well-defined theoretical domains (‘focused meta-analysis’). We also suggest ways for better integration of information about species biology and ecosystem characteristics (‘invasion syndromes’). We expect that a resulting theory of invasions will need to be conceived as a somewhat heterogeneous conglomerate of elements of varying generality and predictive power: laws that apply to well-specified domains, general concepts and theoretical frameworks that can guide thinking in research and management, and in-depth knowledge about the drivers of particular invasions.