  The localization properties of electron states in the quantum Hall regime are
reviewed. The random Landau model, the random matrix model, the tight-binding
Peierls model, and the network model of Chalker and Coddington are introduced.
Descriptions in terms of equivalent tight-binding Hamiltonians, and the 2D
Dirac model, are outlined. Evidences for the universal critical behavior of the
localization length are summarized. A short review of the supersymmetric
critical field theory is provided. The interplay between edge states and bulk
localization properties is investigated. For a system with finite width and
with short-range randomness, a sudden breakdown of the two-point conductance
from $ne^{2}/h$ to 0 ($n$ integer) is predicted if the localization length
exceeds the distance between the edges.
