In the non linear realm, a powerful way to describe complex shapes is in terms of stratifications, that is topological disks together with the proper incidences, so as to define some kind of complex (cell, CW, etc). In particular, singularity theory provides a convenient way to specify such incidences through local normal forms, the parametric form of the topological disks depending on the particular problem investigated. We shall review two examples illustrating this framework in 3D : the detection of loci of extremal curvature of smooth surfaces (the so-called ridges), and the calculation of the Morse-Smale complex of the distance function to points in 3D space (the so-called flow complex). We shall conclude with perspectives arising in trying to generalize such approaches in higher dimension.