  Stable and unstable nuclei with neutron excess ($N>Z$) show - in the
isovector dipole transition strength distribution - a small hump around the
neutron emission threshold energy known as Pygmy Dipole Resonance (PDR). One of
its main features is the isospin mixing allowing the experimental studies with
both isovector and isoscalar probes. Different theoretical approaches and
methodologies are used to deduce the characteristics of the PDR. In this
Chapter, the various mean-field theories and their extensions, devoted to
understand and reproduce the strength distribution of these low-lying dipole
states, are summarised. Special attention is dedicated to the calculations of
the inelastic cross section, aspect that is particularly important in the
investigation with isoscalar probes, such as $\alpha$-particles or $^{17}$O.
The relevance of the radial form factors is presented in relation to the
inelastic cross-section calculations.
