  We discuss the dynamics of magnetic moments in d-wave superconductors, in
particular we focus on moments induced by doping non-magnetic impurities into
cuprates. The interaction of such moments with the Bogoliubov quasiparticles of
the superconductors can be decribed by variants of the pseudogap Kondo model,
characterized by a power-law density of states at the Fermi level. The
Numerical Renormalization Group technique is employed to investigate this Kondo
problem for realistic band structures and particle-hole asymmetries, both at
zero and finite temperatures. In particular, we study the boundary quantum
phase transition between the local-moment and the asymmetric strong-coupling
phases, and argue that this transition has been observed in recent nuclear
magnetic resonance experiments. We determine the spectral properties of both
phases, the location of the critical point as function of Kondo coupling and
doping, and discuss the quantum-critical cross-overs near this phase
transition. In addition, the changes in the local density of states around the
impurity are calculated as function of temperature, being relevant to scanning
tunneling microscopy experiments.
