Until recently, the precise gap function Delta(k) of many nodal superconductors has been unknown. The most notable exception are the high-temperature cuprate superconductors for which angular resolved photoemission spectroscopy and Josephson interferometry have succeeded to clearly identify d(x2-y2)-wave symmetry. Unfortunately, it has turned out to be difficult to apply these methods to some of the other nodal superconductors. Recently it has been recognized that the quasiparticle spectrum of nodal superconductors in the vortex state is very sensitive to the symmetry of the gap function. In particular, Izawa et al. have succeeded in identifying an f-wave order parameter in Sr2RuO4, d(x2-y2)-wave order in CeCoIn5 and kappa-(ET)(2)Cu(NCS)(2), and s+g-wave superconductivity in YNi2B2C and PrOs4Sb12. In this paper we review some of the surprises that were encountered in this exploration. (C) 2004 Elsevier B.V. All rights reserved.