  An overview of the random network model invented by Chalker and Coddington,
and its generalizations, is provided. After a short introduction into the
physics of the Integer Quantum Hall Effect, which historically has been the
motivation for introducing the network model, the percolation model for
electrons in spatial dimension 2 in a strong perpendicular magnetic field and a
spatially correlated random potential is described. Based on this, the network
model is established, using the concepts of percolating probability amplitude
and tunneling. Its localization properties and its behavior at the critical
point are discussed including a short survey on the statistics of energy levels
and wave function amplitudes. Magneto-transport is reviewed with emphasis on
some new results on conductance distributions. Generalizations are performed by
establishing equivalent Hamiltonians. In particular, the significance of
mappings to the Dirac model and the two dimensional Ising model are discussed.
A description of renormalization group treatments is given. The classification
of two dimensional random systems according to their symmetries is outlined.
This provides access to the complete set of quantum phase transitions like the
thermal Hall transition and the spin quantum Hall transition in two dimension.
The supersymmetric effective field theory for the critical properties of
network models is formulated. The network model is extended to higher
dimensions including remarks on the chiral metal phase at the surface of a
multi-layer quantum Hall system.
