Ab-initio predictions of nuclei with masses up to A∼100 or more are 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.A second and major challenge to ab-initio theory is that standard implementations of the above methods are limited to doubly closed (sub-)shell nuclei and to their immediate neighbors [23,14]. As one increases the nuclear mass, longer chains of truly open shell nuclei emerge that cannot be accessed with these approaches. Many-body techniques that could tackle genuine open shell systems-or, at least, singly open shells-would immediately extend the reach of ab-initio studies from a few tens to several hundreds of mid-mass isotopes. Our collaboration has proposed to exploit ideas based on breaking particle-number symmetry in order to achieve this goal [24,25,26]. This has led to reformulating the SCGF in the Gorkov formalism (Gorkov-GF) [26,27,28], which will be discussed in this talk. Applications of Gorkov-GF have been successful for the Ca and neighbouring isotopes up to 54 Ti [29]. Recently, similar developments have also been introduced within the IMSRG framework [13].The last challenge to theory is to provide consistent descriptions of the structure and reactions of nuclei in order to constrain and improve the analysis of experimental data. Microscopic calculations of elastic nucleon scattering were achieved, e.g., for a 16 O target in [30,31]. Recently, ab-initio calculations, including cluster projectiles, have been possible for few-body targets by combining the ab-initio no-core shell model (NCSM) with the resonating-group method (RGM) [32,33]. For larger masses, the SCGF becomes the method of choice due to the equivalence between the many-body self-energy and Fesbach theory of elastic scattering. This fact has guided recent advances of phenomenological dispersive optical models (DOM) [34,35] and microscopic calculations of optical potentials [2,30,36]. Further developing these approaches to proper ab-initio methods will be crucial to advance our understanding of exotic radioactive beam experiments.This talk reports about recent progress on the above topics within the SCGF approach to quantum many-body physics. The new details of the formalis...