The study of dynamics in multiferroic systems is concerned with understanding the time evolution of the coupling between various ferroic orders, in particular under external applied fields. Current research in this field is motivated both by the promise of new types of application reliant on the coupled nature of the dynamics, and the search for new physics lying at the heart of the fundamental understanding of the elementary MF excitations. An increasing number of studies of MF dynamics are concerned with the coupling between electric and magnetic order parameters in the magnetoelectric multiferroics. In this class of materials, the leading research is exploring, both theoretically and experimentally, the fundamental limits (e.g. intrinsic coupling velocity, coupling strength, materials synthesis) of the dynamical magnetoelectric coupling and how these may be both reached and exploited for the development of new technologies.