Legendrian links are topological links that satisfy an extra geometrical condition imposed by a contact structure. Many beautiful and interesting topological links can be made from linking unknotted components; I will focus on special Legendrian versions of such links. I will show how it is possible to associate invariant polynomials to these Legendrian links through the theory of generating families. I will also discuss how these polynomials are closely correlated to the Chekanov polynomials that are defined through the theory of holomorphic curves.