  We review the scaling theory of disordered itinerant electrons with e-e
interactions. We first show how to adjust the microscopic Fermi-liquid theory
to the presence of disorder. Then we describe the non-linear sigma model (NLSM)
with interactions (Finkel'stein's model). This model is closely connected to
the Fermi liquid, but is more generally applicable, since it can also be viewed
as a minimal effective functional describing disordered interacting electrons.
Our discussion emphasizes the general structure of the theory, and the
connection of the scaling parameters to conservation laws. We then move on to
discuss the metal-insulator transition (MIT) in the disordered electron liquid
in two and three dimensions. This MIT is a non-trivial example of a quantum
phase transition. The NLSM approach allows to identify the dynamical exponent
connecting the spatial and energy scales, which is central for the description
of the kinetic and thermodynamic behavior in the critical region of the MIT in
three dimensions. In two dimensions, the system can be discussed in terms of a
flow in the disorder-interaction phase plane, which is controlled by a fixed
point. We demonstrate that the two-parameter RG-equations accurately describe
electrons in Si-MOSFETs including the observed non-monotonic behavior of the
resistance and its strong drop at low temperatures. The theory can also be
applied to systems with an attractive interaction in the Cooper channel, where
it describes the suppression of superconductivity in disordered amorphous
films. We extend our discussion to heat transport in the two-dimensional
electron liquid. Similar to the electric conductivity, the thermal conductivity
also acquires logarithmic corrections induced by electron interaction and
disorder. The resulting thermal conductivity can be calculated in the NLSM
formalism after introducing so-called gravitational potentials.
