We dene two modal logics that allow to reason about modications of graphs. Both have a universal modal operator. The rst one only involves global modications (of some state label, or of some edge label) everywhere in the graph. The second one also allows for modications that are local to states. The global version generalizes logics of public announcements and public assignments, as well as a logic of preference modication introduced by van Benthem et Liu. By means of reduction axioms we show that it is just as expressive as the underlying logic without global modiers. We then show that adding local modiers dramatically increases the power of the logic: the logic of global and local modiers is undecidable. We nally study its relation with hybrid logic with binder.