Due to Alexander, it is well known that every closed oriented 3-manifold has an open book decomposition. In this talk, we will discuss the importance of the open book decompositions in manifold theory, in paticular in contact geometry. After a brief introduction on contact 3-manifolds, we will focus on a class of knots called Legendrian knots. We will define a new invariant for Legendrian knots using open book decompositions. We define the support genus sg(L) of a Legendrian knot L in a contact manifold M as the minimal genus of a page of an open book of M supporting the contact structure such that L sits on a page and the framings given by the contact structure and the page agree. We will discuss the applications of this invariant and list several open problems related to support genus of Legendrian knots.