$p$-adic period spaces have been introduced by Rapoport and Zink as a generalization of Drinfeld upper half spaces and Lubin-Tate spaces. Those are open subsets of a rigid analytic $p$-adic flag manifold. An approximation of this open subset is the so called weakly admissible locus obtained by removing a profinite set of closed Schubert varieties. I will explain a recent theorem characterizing when the period space coincides with the weakly admissible locus. The proof consists in a thorough study of modifications of G-bundles on the curve.