  This review is intended to give a pedagogical and unified view on the subject
of the statistics and scaling of physical quantities in disordered electron
systems at very low temperatures. Quantum coherence at low temperatures and
randomness of microscopic details can cause large fluctuations of physical
quantities. In such mesoscopic systems a localization-delocalization transition
can occur which forms a critical phenomenon. Accordingly, a one-parameter
scaling theory was formulated stressing the role of conductance as the
(one-parameter) scaling variable. However, the notion of an order parameter was
not fully clarified in this theory. Based on presently available analytical and
numerical results we focus here on the description of the total distribution
functions and their flow with increasing system size. Still, one-parameter
scaling theory does work in terms of typical values of the local density of
states and of the conductance which serve as order parameter and scaling
variable of the localization-delocalization transition, respectively. Below a
certain length scale, $\xi_c$, related to the value of the typical conductance,
local quantities are multifractally distributed. This multifractal behavior
becomes universal on approaching the localization-delocalization transition
with $\xi_c$ playing the role of a correlation length.
