TITLE: Hironaka desingularisation theorem -- new proofs in literature?
QUESTION [19 upvotes]: I'm wondering what the landscape looks like for proofs of Hironaka's desingularisation theorem.

Are there many proofs in the literature?
Is there a commonly accepted simplest bare-knuckle proof out there
that might be considered a pleasant read for people outside of
algebraic geometry?
Would that still be Hironaka's original manuscript?

REPLY [3 votes]: Old thread, but let me point out the recent preprint Very fast, very functorial, and very easy resolution of singularities, by M. McQuillan and G. Marzo.
There is a also published version on GAFA, with McQuillan listed as the only author.