Beyond the Standard Model (BSM) theories aim to explain some of the missing ingredients of the Standard Model, yet no clear evidence for any of them has been found so far. Furthermore, most of these models introduce many new parameters, and make strong predictions for a multitude of experimental searches in particle physics, astrophysics and cosmology. Therefore, contrasting these theories with experimental data requires smart strategies to sample complicated parameter spaces and perform rigorous combinations of experimental results from many sources. In this talk I will introduce GAMBIT, a tool developed to make statistical studies of BSM theories easy and fast, and allow the study of models with many parameters and multiple experimental searches. I will also show the results of various global studies of dark matter and supersymmetric models, where I will focus on their survival status in light of recent data and also on highlighting potential strategies to explore the remaining unconstrained parameter regions.