The independent complex of a matroid is a shellable simplicial complex: their facets can be ordered nicely, which translates to interesting properties in algebra and combinatorics. Simon in 1994 conjectured that any shellable complex can be extended to the k-skeleton of a simplex while maintaining the shelling property. We go over various tools and results related to this problem. In particular, we will be going over a recent joint work with M. Coleman, A. Dochtermann and N. Geist on proving this conjecture for a smaller class, which contains the entire class of matroids.