Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)In this article some qualitative and geometric aspects of non-smooth dynamical systems theory are discussed. The main aim of this article is to develop a systematic method for studying local (and global) bifurcations in non-smooth dynamical systems. Our results deal with the classification and characterization of generic codimension-2 singularities of planar Filippov Systems as well as the presentation of the bifurcation diagrams and some dynamical consequences. (c) 2010 Elsevier Inc. All rights reserved.250419672023Spanish MCyT/FEDER [MTM2009-06973]Catalan SGR [2009SGR859]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Spanish PhD grant [FPU AP2005-1314]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Spanish MCyT/FEDER [MTM2009-06973]Catalan SGR [2009SGR859]FAPESP [2007/06896-05]Spanish PhD grant [FPU AP2005-1314]