We discuss how Furstenberg--Zimmer structure theory and Mackey theory can be generalized to the setting of uncountable discrete groups and inseparable spaces. We put an emphasis on the technical innovations (and simplifications) in this generalization process, in particular the application of topos-theoretic techniques in the form of conditional analysis to structural ergodic theory. The talk is partially based on joint works with Terence Tao. If time permits, we will also present results from an ongoing collaboration with Pieter Spaas on a noncommutative version of certain results in Furstenberg--Zimmer structure theory.