An overview of some recent work concerning the singular behavior of electromagnetic fields at edges and tips in bi-isotropic and some bianisotropic materials is presented. Special emphasis will be placed on the singular behavior at the tip of concentric metal cones embedded in a special bianisotropic material. Some new results for this case are presented. Finally, some general conclusions regarding the effect of chirality and anisotropy are discussed. ¿ American Geophysical Union 1995