In this chapter, we present results on dynamic modal operators that can change the accessibility relation of a model during the evaluation of a formula. In particular, we extend the basic modal language with modalities that are able to delete, add or swap an edge between pairs of elements in the domain of a model. We define a generic framework to characterize this kind of operations. First, we investigate relation-changing modal logics as fragments of other, better investigated, logics, and in particular provide equivalence preserving translations into first order logic and hybrid logic. To investigate their expressive power, we define suitable notions of bisimulation for the logics introduced. We then turn to the complexity of different reasoning problems for these kind of logics. Finally, we discuss existing Hilbert-style axiomatizations, and the special techniques needed to establish completeness.