Event Structures (ESs) address the representation of direct relationships between individual events, usually capturing the notions of causality and conflict. Up to now, such relationships have been static, i.e. they cannot change during a system run. Thus the common ESs only model a static view on systems. We dynamize causality such that causal dependencies between some events can be changed by occurrences of other events. We first model and study the case in which events may entail the removal of causal dependencies, then we consider the addition of causal dependencies, and finally we combine both approaches in the so-called Dynamic Causality ESs. For all three newly defined types of ESs, we study their expressive power in comparison to the well-known Prime ESs, Dual ESs, Extended Bundle ESs, and ESs for Resolvable Conflicts. Interestingly Dynamic Causality ESs subsume Extended Bundle ESs and Dual ESs but are incomparable with ESs for Resolvable Conflicts.