W. Thurston proved that many 3-manifolds are hyperbolic or can be decomposed into hyperbolic pieces (Hyperbolization Theorem). Even though the hyperbolic structure of a particular manifold can be calculated, it is often hard to relate it to a topological or combinatorial description of the manifold. For link complements in 3-sphere, such a description can be given in a simple form, by a link diagram. We will introduce an alternative method for computing hyperbolic structures of links (joint with Thistlethwaite). The method allows the computation directly from a link diagram, not triangulating the manifold. We will discuss how this helps to compute the exact hyperbolic volume, arithmetic invariants (with Neumann), the representation and character variety (with Culler and Peterson), and to make general observations about the intrinsic geometry from a link diagram.