  We present the basic concepts and recent developments in the time-dependent
density functional theory (TDDFT) for describing nuclear dynamics at low
energy. The symmetry breaking is inherent in nuclear energy density functionals
(EDFs), which provides a practical description of important correlations at the
ground state. Properties of elementary modes of excitation are strongly
influenced by the symmetry breaking and can be studied with TDDFT. In
particular, a number of recent developments in the linear response calculation
have demonstrated their usefulness in description of collective modes of
excitation in nuclei. Unrestricted real-time calculations have also become
available in recent years, with new developments for quantitative description
of nuclear collision phenomena. There are, however, limitations in the
real-time approach; for instance, it cannot describe the many-body quantum
tunneling. Thus, we treat the quantum fluctuations associated with slow
collective motions assuming that time evolution of densities are determined by
a few collective coordinates and momenta. The concept of collective submanifold
is introduced in the phase space associated with the TDDFT and used to quantize
the collective dynamics. Selected applications are presented to demonstrate the
usefulness and quality of the new approaches. Finally, conceptual differences
between nuclear and electronic TDDFT are discussed, with some recent
applications to studies of electron dynamics in the linear response and under a
strong laser field.
