The theory of perfectoid rings is a powerful tool for studying algebraic geometry in mixed characteristic, but it heavily relies on delicate nature of non-Noetherian rings. To establish a general framework to apply the perfectoid theory in a Noetherian setting, we introduce a certain class of sequences of ring extensions that provide Noetherian approximation of perfectoid rings. We then discuss their “tilts” and illustrate some application to log-regular rings. This talk is based on a joint work with Shinnosuke Ishiro and Kazuma Shimomoto.