Multifractality at conventional and unconventional Anderson transitions F. Evers Institut fuer Nanotechnologie, Forschungszentrum Karlsruhe, 76021 Karlsruhe, Germany and Institut fuer Theorie der Kondensierten Materie, Universitaet Karlsruhe, 76128 Karlsruhe, Germany Metals can be turned into insulators by tuning external control parameters, like the impurity concentration, pressure or a magnetic field, in the case of a quantum Hall transition. In recent years, our classification scheme of the various possible transitions has experienced considerable improvement. Howevers, while various classes of such "Anderson transitions" have been identified, detailed understanding of their individual properties is still lacking. All Anderson transitions have in common that right at the critical point, the wavefunctions have unusual statistical properties: their moments $\langle |\psi|^{2q}\rangle$ scale with the system size exhibiting a set of non-trivial exponents, the "multifractality spectrum" $\tau_q$. This spectrum is a unique characterists of the transition; it can be measured in principle and also it can provide crucial details about the structure of the underlying low energy theory. In our talk we shall give a very brief introduction into the concept of multifactality together with a short review of the modern classification of disordered metals. Thereafter, we shall discuss recent numerical and analytical results on the spin quantum Hall transition together with an extension of the concept to surface multifractality. Finally, it is intended to present most recent analytical predictions and numerical checks on "selforganized criticality" in the graphene system. Work was done in collaboration with Achim Mildenberger and Alexander Mirlin.