Resolution of singularities for the dynamical mathematician

I begin by explaining to non-specialists why resolution of singularities in characteristic 0 works. Then I go into some ideas telling how it actually works. I finish with a brief discussion of related results on foliations. I report on work with André Belotto da Silva, Michael Temkin, and Jarosław Włodarczyk; any claim to originality is joint with them and appears in the paper [AdSTW25].