  We review the notion of symmetry breaking and restoration within the frame of
nuclear energy density functional methods. We focus on key differences between
wave-function- and energy-functional-based methods. In particular, we point to
difficulties to formulate the restoration of symmetries within the energy
functional framework. The problems tackled recently in connection with
particle-number restoration serve as a baseline to the present discussion.
Reaching out to angular-momentum restoration, we identify an exact mathematical
property of the energy density $E^{LM}(\vec{R})$ that could be used to
constrain energy density functional kernels. Consequently, we suggest possible
routes towards a better formulation of symmetry restorations within energy
density functional methods.
