The Global and Modular Beyond-Standard Model Inference Tool (GAMBIT) is an open source software framework for performing global statistical fits of particle physics models, using a wide range of particle and astroparticle data. In this review, we describe the design principles of the package, the statistical and sampling frameworks, the experimental data included, and the first two years of physics results generated with it. This includes supersymmetric models, axion theories, Higgs portal dark matter scenarios and an extension of the Standard Model to include right-handed neutrinos. Owing to the broad spectrum of physics scenarios tackled by the GAMBIT community, this also serves as a convenient, self-contained review of the current experimental and theoretical status of the most popular models of dark matter.