This paper describes some of the challenges and opportunities when deploying static and dynamic analysis at scale, drawing on the authors' experience with the Infer and Sapienz Technologies at Facebook, each of which started life as a research-led start-up that was subsequently deployed at scale, impacting billions of people worldwide. The paper identifies open problems that have yet to receive significant attention from the scientific community, yet which have potential for profound real world impact, formulating these as research questions that, we believe, are ripe for exploration and that would make excellent topics for research projects. Note: This paper accompanies the authors' joint keynote at the 18th IEEE International Working Conference on Source Code Analysis and Manipulation, September 23rd-24th, 2018 - Madrid, Spain.