  We review recent applications of the real-space renormalization group (RG)
approach to the integer quantum Hall (QH) transition. The RG approach, applied
to the Chalker-Coddington network model, 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) at energies away from the
transition yields a value of the critical exponent, nu_G=2.39 +/- 0.01, that
agrees with most accurate large-size lattice simulations. Analyzing the
evolution of the distribution of phases of the transmission coefficients upon a
step of the RG transformation, we obtain information about the energy-level
statistics (ELS). From the fixed point of the RG transformation we extract a
critical ELS. Away from the transition the ELS crosses over towards a Poisson
distribution. Studying the scaling behavior of the ELS around the QH
transition, we extract the critical exponent nu_ELS=2.37 +/- 0.02.
