In this thesis we study the simplification of triangular and tetrahedral meshes by the use of techniques based on successive edge collapses, as well as the exploitation of the generated multiple levels of detail (progressive meshes) for the effective processing of the models. Regarding triangular meshes, we present a method for the construction of progressive hulls, by suitable edge collapses. We use the generated hulls for the acceleration of intersection tests between the initial mesh and a line. Regarding tetrahedral meshes, we simplify meshes with associated vector fields. We construct progressive tetrahedral meshes by taking into account, while collapsing edges, both the geometry of the mesh and the associated field.