The Kazhdan-Lusztig polynomial of a matroid was introduced by Elias, Proudfoot and Wakefield, analogous to the classical Kazhdan-Lusztig polynomial of the symmetric group. There are many interesting conjectures and open problems concerning the matroid Kazhdan-Lusztig polynomials. In this talk we will introduce some of these conjectures and review some progress on the Kazhdan-Lusztig polynomials for fan matroids, whirl matroids, wheel matroids, and uniform matroids. This is based on some joint work with Alice Gao, Linyuan Lu, Matthew Xie and Philip Zhang.