Abstract: The prismatic site for a p-adic formal scheme was recently introduced by Bhatt-Scholze. The certain sheaves on this site give rise to some canonical objects in the classical p-adic Hodge theory. Let X be a smooth formal scheme over Zp. In my talk, I will introduce and study the de Rham crystal (i.e. the modules over a certain sheaf of rings satisfying some rigid condition) over X, and explain how it is related with the classical de Rham local systems (on the generic fiber of) X and Fontaine's regular connection.