I will describe recent progress in developing a general framework for accurate ground-state calculations of interacting electronic systems. This framework is based on the use of auxiliary-fields, and addresses the sign problem (which turns into a phase problem for realistic electron-electron interactions) by constraining the imaginary-time paths with an approximate sign (gauge) condition. The approach can be used to study either a fully materials-specific Hamiltonian or a Hubbard-like model --- or indeed any electronic Hamiltonian in between as the former is ``down-folded'' to the latter. As an example of materials-specific calculations, we determine the equation of state in a variety of solids, which systematically removes deficiencies of density-functional theory (DFT) results. As an example of model studies, the nature of magnetic and charge correlations in the doped Hubbard model are determined, in the context of models for high-temperature superconductivity. Its implications on the search for so-called FFLO phases with cold atoms will be discussed. We also present exact results on the properties of the two-dimensional ultracold Fermi gas. Calculations in systems with strong spin-orbit coupling will be discussed.