Abstract: Joint work in progress with Johannes Anschütz, Arthur-César Le Bras and Guido Bosco. The analytic de Rham stack is a new construction in analytic geometry (after Clausen and Scholze) whose theory of quasi-coherent sheaves encodes a notion of p-adic D-modules, but that has the virtue that it can be defined even under lack of differentials (eg. for perfectoid spaces or Fargues-Fontaine curves). In this talk I will mention some (expected) applications of the theory of the analytic de Rham stack in p-adic Hodge theory in the form of Fargues-Fontaine de Rham stacks; analytic objects whose cohomology theories refine the usual de Rham cohomology of rigid spaces in the form of the Fargues-Fontaine de Rham cohomology of Le Bras-Vezzani.