  We present the extension of Frozen Density Embedding (FDE) theory to
real-time Time Dependent Density Functional Theory (rt-TDDFT). FDE a is
DFT-in-DFT embedding method that allows to partition a larger Kohn-Sham system
into a set of smaller, coupled Kohn-Sham systems. Additional to the
computational advantage, FDE provides physical insight into the properties of
embedded systems and the coupling interactions between them. The extension to
rt-TDDFT is done straightforwardly by evolving the Kohn-Sham subsystems in time
simultaneously, while updating the embedding potential between the systems at
every time step. Two main applications are presented: the explicit excitation
energy transfer in real time between subsystems is demonstrated for the case of
the Na$_4$ cluster and the effect of the embedding on optical spectra of
coupled chromophores. In particular, the importance of including the full
dynamic response in the embedding potential is demonstrated.
