Proof of Thurston's geometrization conjecture has been a major achievement in the study of 3-manifolds and proves the existence of natural geometric structures on compact 3-manifolds. However this proof and the mere knowledge of the existence of such structures does not give a description of the geometry and therefore fails to answer many of the existing questions. We discuss a project that attempts to find an effective solution to the geometrization and therefore produces models of the promised hyperbolic structures. We explain how this can be used to answer a number of unanswered questions and relate topological and geometrical properties of the manifold.