  We review recent results based on an application of the real-space
renormalization group (RG) approach to a network model for the integer quantum
Hall (QH) transition. We demonstrate that this RG approach reproduces the
critical distribution of the power transmission coefficients, i.e.,
two-terminal conductances, P_c(G), with very high accuracy. The RG flow of P(G)
yields a value of the critical exponent nu that agrees with most accurate
large-size lattice simulations. A description of how to obtain other relevant
transport coefficients such as R_L and R_H is given. From the non-trivial fixed
point of the RG flow we extract the critical level-spacing distribution (LSD)
which is close, but distinctively different from the earlier large-scale
simulations. We find that the LSD obeys scaling behavior around the QH
transition with nu=2.37\pm 0.02. Away from the transition it changes towards
the Poisson distribution. We next investigate the plateau-to-insulator
transition. For a fully quantum coherent situation, we find a quantized Hall
insulator with R_H ~ h/e^2 up to R_L ~ 20 h/e^2 when interpreting the results
in terms of the most probable value of the distribution P(R_H). Upon further
increasing R_L, the Hall insulator with diverging R_H ~ R_L^kappa is seen. This
crossover depends on the precise nature of the averaging of P(R_L) and P(R_H).
We also study the effect of long-ranged inhomogeneities on the critical
properties of the QH transition modeled by a power law correlation in the
random potential. Similar to the classical percolation, we observe an
enhancement of nu with decreasing correlation range. These results exemplify
the surprising fact that a small RG unit, containing five nodes, accurately
captures most of the correlations responsible for the QH transition.
