We will present the definition of Hyodo-Kato stacks, which intuitively are de Rham stacks of relative Fargues--Fontaine curves. After explaining their basic properties, we will present a new proof of the $p$-adic monodromy theorem, which avoids any deeper analysis of $p$-adic differential equations. This talk is based on joint work with Bosco/Le Bras/Rodriguez-Camargo/Scholze.
