Precision calculations in de Sitter space (such as of inflationary predictions for primordial fluctuations) are often plagued by infrared problems and issues of secular time dependence. Similar issues about the breakdown of perturbation theory also arise for information loss in black holes. This talk briefly summarizes what is known about when these problems do (and do not) arise, and how similar problems are dealt with in other areas (like optics). It is argued that Master-Equation techniques used there also apply to cosmology (and possibly black holes) and can tell us how to extract reliably late-time predictions. Applied to inflation they lead to Starobinsky's stochastic methods (plus potential corrections). This is argued to provide an explanation for why stochastic inflation seems to resum IR effects in simple examples, and allows these tools to be generalized to other systems. I mention in passing the relevance of these tools to the problem of Schrodinger's Cosmologist: how primordial fluctuations decohere sometime between their production during inflation and their observation early in the present Big Bang Epoch.