  Self-consistent mean-field models are a powerful tool in the investigation of
nuclear structure and low-energy dynamics. They are based on effective
energy-density functionals, often formulated in terms of effective
density-dependent nucleon-nucleon interactions. The free parameters of the
functional are adjusted to empirical data. A proper choice of these parameters
requires a comprehensive set of constraints covering experimental data on
finite nuclei, concerning static as well as dynamical properties, empirical
characteristics of nuclear matter, and observational information on
nucleosynthesis, neutron stars and supernovae. This work aims at a
comprehensive survey of the performance of one of the most successful
non-relativistic self-consistent method, the Skyrme-Hartree-Fock model (SHF),
with respect to these constraints. A full description of the Skyrme functional
is given and its relation to other effective interactions is discussed. The
validity of the application of SHF far from stability and in dense environments
beyond the nuclear saturation density is critically assessed. The use of SHF in
models extended beyond the mean field approximation by including some
correlations is discussed. Finally, future prospects for further development of
SHF towards a more consistent application of the existing and promisingly newly
developing constraints are outlined.
