"Algebraic Number Theory and Related Topics 2014". December 1～5, 2014. edited by Takeshi Tsuji, Hiroki Takahashi and Yuichiro Hoshi. The papers presented in this volume of RIMS Kôkyûroku Bessatsu are in final form and refereed. / In this survey article, we explain the contents of [Sch, §1-§7]. Our main aim is to introduce the definition of perfectoid space and the outline of the proof of the tilting equivalence due to Scholze.