In 1995, de Jong proved the existence of regular alterations in arbitrary characteristic. I would like to have a little survey of important applications of this theorem, e.g. things you could do if you had resolution of singularities, but for which alterations are sufficient.
I am aware of the 1996 Bourbaki article by Berthelot, however I guess that many new developments have taken place since then.
There is a book, Resolution of Singularities — A research textbook in tribute to Oscar Zariski, edited by Hauser, Lipman, Oort and Quiros (Progress in Mathematics, Birkhäuser, 2000). There, you'll get four papers related to alterations : one by Abramovich and Oort that explains De Jong's theorem, one by Geisser that gives alterations, and another by De Jong himself about Dieudonné modules, and finally one by Pop on birational anabelian geometry.
It is (in the form of Gabber's generalisation) applied in Luc Illusie, Yves Laszlo, Fabrice Orgogozo, Travaux de Gabber sur l'uniformisation locale et la cohomologie etale des schemas quasi-excellents https://arxiv.org/abs/1207.3648 to finiteness statements and purity in étale cohomology.
