In the search for clues to the matter-antimatter puzzle, experiments with atoms or molecules play a particular role. These systems allow measurements with very high precision, as demonstrated by the unprecedented limits down to 10-30 e cm on electron EDM using molecular ions, and relative measurements at the level of 10-12 in spectroscopy of antihydrogen atoms. Building on these impressive measurements, new experimental directions offer potential for drastic improvements. We review here some of the new perspectives in those fields and their associated prospects for new physics searches. This article is part of the theme issue 'The particle-gravity frontier'.