  Ab-initio predictions of nuclei with masses up to A~100 or more is becoming
possible thanks to novel advances in computations and in the formalism of
many-body physics. Some of the most fundamental issues include how to deal with
many-nucleon interactions, how to calculate degenerate--open shell--systems,
and pursuing ab-initio approaches to reaction theory. Self-consistent Green's
function (SCGF) theory is a natural approach to address these challenges. Its
formalism has recently been extended to three- and many-body interactions and
reformulated within the Gorkov framework to reach semi-magic open shell
isotopes. These exciting developments, together with the predictive power of
chiral nuclear Hamiltonians, are opening the path to understanding large
portions of the nuclear chart, especially within the $sd$ and $pf$ shells. The
present talk reviews the most recent advances in ab-initio nuclear structure
and many-body theory that have been possible through the SCGF approach.
