We will first talk about the recent result of Diao-Lan-Liu-Zhu on the p-adic analogue of Riemann-Hilbert correspondence, and explain how it is linked with problems related to p-adic local Langlands, such as Fontaine-Mazur conjecture. Then we will talk about our joint work with Tong Liu proving that every relative crystalline representation with Hodge-Tate weights in $$0, 1$$ arises from a p-divisible group if the ramification is small, and explain its application to studying the correspondence.