Resolution of singularities of complex algebraic varieties and their families

We discuss Hironaka's theorem on resolution of singularities in charactetistic 0 as well as more recent progress, both on simplifying and improving Hironaka's method of proof and on new results and directions on families of varieties, leading to joint work on toroidal orbifolds with Michael Temkin and Jaros{\l}aw W{\l}odarczyk.
Comment: 20 pages, submitted to proceedings of the ICM, Rio 2018