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 nonsymmetry-broken situation where a quantum phase transition toward 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.