These notes serve as an expository survey of the propagation of singularities theorem with small regularity loss on dynamical systems with normally hyperbolic trapping proved in Jia Q Propagation of Singularity with Normally Hyperbolic Trapping. Preprint, arXiv:2206.04820 (2022)), which is a refinement of (Probability And Mathematical Physics. 2:71–126). In particular, this can be applied to wave equations on Kerr and Kerr-de Sitter spacetimes.