From dark matter and dark energy, to neutrino oscillations and the lack of antimatter in the universe, there is growing evidence that the Standard Model is incomplete. Complementary to explorations at the high-energy frontier, there is a burgeoning community looking for new physics at the precision frontier, where Beyond Standard Model (BSM) physics may appear as small deviations from expected results in experiments with atoms and nuclei. Tests of Quantum Electrodynamics (QED) with few-electron systems offer one of the most promising avenues for looking for new physics, as QED is the best understood field theory and extremely precise predictions can be obtained for few-electron systems. Tantalising discrepancies have appeared in the so-called “proton-radius puzzle”, and the new 4.5 sigma difference with the QED prediction for the fine structure of postronium. I will present a new, alternative method for QED tests and BSM searches with exotic muonic and antiprotonic atoms, show first results, and discuss the complementarity with ongoing metrology measurements and nuclear physics studies.