  Motivated by both experimental and theoretical activities, we discuss the
fate of Kondo screening and possible quantum phase transitions in
antiferromagnetically ordered phases of Kondo lattices. While transitions with
topological changes of the Fermi surface may occur, we demonstrate that an
entirely continuous evolution from itinerant to local-moment antiferromagnetism
(i.e. from strong to negligible Kondo screening) is possible as well. This
situation is in contrast to that in a non-symmetry-broken situation where a
quantum phase transition towards an exotic metallic spin-liquid state
necessarily accompanies the disappearance of Kondo screening. We discuss
criteria for the existence of topological transitions in the antiferromagnetic
phase, as well as implications for theoretical scenarios and for current
experiments.
