Given the plethora of competing Beyond-the-Standard-Model (BSM) theories, we need to make the best possible use of all current and upcoming experimental results to help guide the search for BSM physics. In this conference paper I discuss how BSM global fits are key in this effort, and what the main challenges of such analyses are. I give brief introductions to the model-independent GAMBIT framework for BSM global fits and the recently released GAMBIT Universal Model Machine (GUM), which uses Lagrangian-level tools to automatically set up a GAMBIT global fit starting from a BSM Lagrangian.