Many application areas in CAD/CAM are concerned with triangulation of surfaces, and require an error bounded approximation of a parametric surface model. In this paper we present an overview of the authors results on surface meshing. Two methods are described for triangulating objects bounded by trimmed parametric surfaces. The algorithms approximate the object with a predefined tolerance, and are adaptive to the surface curvature. The main difference between the two algorithms lies on the way that adaption is achieved. While the first method takes into account isotropic bounds of the surface curvature associated to each parametric point, the second algorithm uses bounds that do depend on the curvature direction. Emphasis is made on the computation of the curvature-based bounds and on the triangulation of the interior of the faces. Examples are presented, and results are analyzed comparing the two algorithms. Finally, open problems are enumerated.