The admissible locus inside the flag variety F(G,mu) for a reductive group G and a minuscule cocharacter mu of G is a p-adic analogue of complex analytic period domains. It is the image of certain period maps and therefore plays an important role in the realization of Langlands correspondences. However, it is in general very hard to understand. On the other hand, it has an algebraic approximation, called the weakly admissible locus, which has an explicit description. In this talk I will explain recent results on the relation between the admissible and the weakly admissible locus.