Calabi-Yau structures on dg categories provide a noncommutative analog of symplectic structures. In this talk I will introduce a noncommutative analog of volume forms called noncommutative Euler structures. I will give some examples of these and relate noncommutative Euler structures to string topology-type operations. An application of these ideas is the proof that the Goresky--Hingston string coproduct on the homology of free loop space is not homotopy invariant. If I have time, I will also discuss how Euler structures give rise to volume forms on derived mapping stacks. This is a report on work in progress joint with Florian Naef.