  This contribution reviews the present status on the available constraints to
the nuclear equation of state (EoS) around saturation density from nuclear
structure calculations on ground and collective excited state properties of
atomic nuclei. It concentrates on predictions based on self-consistent
mean-field calculations, which can be considered as an approximate realization
of an exact energy density functional (EDF). EDFs are derived from effective
interactions commonly fitted to nuclear masses, charge radii and, in many
cases, also to pseudo-data such as nuclear matter properties. Although in a
model dependent way, EDFs constitute nowadays a unique tool to reliably and
consistently access bulk ground state and collective excited state properties
of atomic nuclei along the nuclear chart as well as the EoS. For comparison,
some emphasis is also given to the results obtained with the so called {\it ab
initio} approaches that aim at describing the nuclear EoS based on interactions
fitted to few-body data only. Bridging the existent gap between these two
frameworks will be essential since it may allow to improve our understanding on
the diverse phenomenology observed in nuclei. Examples on observations from
astrophysical objects and processes sensitive to the nuclear EoS are also
briefly discussed. As the main conclusion, the isospin dependence of the
nuclear EoS around saturation density and, to a lesser extent, the nuclear
matter incompressibility remain to be accurately determined. Experimental and
theoretical efforts in finding and measuring observables specially sensitive to
the EoS properties are of paramount importance, not only for low-energy nuclear
physics but also for nuclear astrophysics applications.
