Among the microscopic approaches to the nuclear many-body
problem, energy density functionals (EDF) provide the most
complete and accurate description of ground states and
collective excitations over the whole nuclide chart.
The current generation of relativistic EDFs, using parameters
adjusted to reproduce empirical properties of nuclear matter and
bulk properties of finite nuclei, has been applied to studies of
arbitrarily heavy nuclei, exotic nuclei far from beta-stability, and
systems at the nucleon drip-lines.

In addition to recent advances, future challenges for nuclear
EDFs will be reviewed. Arguably one of the most important is
a fully microscopic foundation based on the underlying theory of
strong interactions. When considering applications, equally important
is to develop EDF-based structure models that go beyond the static
mean-field approximation. Detailed predictions of excitation spectra and
transition rates necessitate the inclusion of correlations related to the
restoration of broken symmetries and to fluctuations of collective variables.