  The multifractal analysis of disorder induced localization-delocalization
transitions is reviewed. Scaling properties of this transition are generic for
multi parameter coherent systems which show broadly distributed observables at
criticality. The multifractal analysis of local measures is extended to more
general observables including scaling variables such as the conductance in the
localization problem. The relation of multifractal dimensions to critical
exponents such as the order parameter exponent $\beta$ and the correlation
length exponent $\nu$ is investigated. We discuss a number of scaling relations
between spectra of critical exponents, showing that all of the critical
exponents necessary to characterize the critical phenomenon can be obtained
within the generalized multifractal analysis. Furthermore we show how bounds
for the correlation length exponent $\nu$ are obtained by the typical order
parameter exponent $\alpha_0$ and make contact between the multifractal
analysis and the finite size scaling approach in 2-d by relying on conformal
mapping arguments.
