Gauge theories play a central role in particle and condensed matter physics. Heavy-ion collisions explore the strong dynamics of quarks and gluons, which also governs the deep interior of neutron stars, while strongly correlated electrons determine the physics of high-temperature superconductors and spin liquids. Numerical simulations of such systems are often hindered by sign problems. In quantum link models - an alternative formulation of gauge theories developed by the applicant - gauge fields emerge from discrete quantum variables. In the past year, in close collaboration with atomic physicists, we have established quantum link models as a framework for the atomic quantum simulation of dynamical gauge fields. Abelian gauge theories can be realized with Bose-Fermi mixtures of ultracold atoms in an optical lattice, while non-Abelian gauge fields arise from fermionic constituents embodied by alkaline-earth atoms. Quantum simulators, which do not suffer from the sign problem, shall be constructed to address non-trivial dynamics, including quantum phase transitions in spin liquids, the real-time dynamics of confining strings as well as of chiral symmetry restoration at finite temperature and baryon density, baryon superfluidity, or color-flavor locking. New classical simulation algorithms shall be developed in order to solve severe sign problems, to investigate confining gauge theories, and to validate the proposed quantum simulators. Starting from U(1) and SU(2) gauge theories, an atomic physics tool box shall be developed for quantum simulation of gauge theories of increasing complexity, ultimately aiming at 4-d Quantum Chromodynamics (QCD). This project is based on innovative ideas from particle, condensed matter, and computational physics, and requires an interdisciplinary team of researchers. It has the potential to drastically increase the power of simulations and to address very challenging problems that cannot be solved with classical simulation methods.