  We summarize recent non-perturbative results obtained for the renormalization
constants computed in the RI'-MOM scheme for $N_{\rm f}=2+1+1$ twisted mass
QCD. Our implementation employs the Iwasaki gauge action and four dynamical
degenerate twisted mass fermions. Renormalization constants for scalar,
pseudo-scalar, vector and axial operators, as well as the quark propagator
renormalization, are computed at three different values of the lattice spacing,
two different volumes and several values of the twisted mass. Our method allows
for a precise cross-check of the running, because of the particular proper
treatment of the hypercubic artifacts. Preliminary results for twist-2
operators are also presented.
