Several major hypotheses have been proposed to explain and predict biological invasions, but the general applicability of these hypotheses is largely unknown, as most of them have not been evaluated using a standard approach across taxonomic groups and habitats. We offer such an evaluation for six selected leading hypotheses. Our global literature review reveals that those hypotheses that consider interactions of exotic invaders with their new environment (invasional meltdown, novel weapons, enemy release) are better supported by empirical evidence than other hypotheses (biotic resistance, island susceptibility, tens rule). We also show that empirical support for the six hypotheses has declined over time, and that support differs among taxonomic groups and habitats. Our results have implications for basic and applied research, policy making, and invasive species management, as their effectiveness depends on sound hypotheses.