It is a result of Thurston that for a large class of knots, there is a unique complete hyperbolic structure on its complement. This leads very naturally to the 3-manifold invariant of hyperbolic volume, the volume of this 3-manifold. In this talk we will discuss motivations of the study of this invariant, as well as examples of how to compute it. We will also discuss drawbacks of volume and introduce further extensions of it, such as the Chern-Simons invariant, and how to describe the volume of families of perturbed manifolds, where the hyperbolic structure is no longer complete.