  We review some of our recent results concerning the relationship between the
Real-Space Renormalization Group method and Quantum Groups. We show this
relation by applying real-space RG methods to study two quantum group invariant
Hamiltonians, that of the XXZ model and the Ising model in a transverse field
(ITF) defined in an open chain with appropriate boundary terms. The quantum
group symmetry is preserved under the RG transformation except for the
appearence of a quantum group anomalous term which vanishes in the classical
case. This is called {\em the quantum group anomaly}. We derive the new qRG
equations for the XXZ model and show that the RG-flow diagram obtained in this
fashion exhibits the correct line of critical points that the exact model has.
In the ITF model the qRG-flow equations coincide with the tensor product
decomposition of cyclic irreps of $SU_q(2)$ with $q^4=1$.
