  We present a survey on the recent progress with desingularization of
quasi-excellent schemes of characteristic zero. Due to expository goals of the
paper we concentrate on giving examples and outlining main ideas, and we refer
to other sources for detailed proofs and technical details. This survey will be
published in the proceedings of the conference "Motivic integration and its
interactions with model theory and non-archimedean geometry" (ICMS, May 2008).
