We will first explain the recent result of Diao-Lan-Liu-Zhu on the p-adic analogue of Riemann-Hilbert correspondence. 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.