High-resolution spectroscopy of the simplest atoms and molecules plays an important role in the determination of fundamental physical constants such as the Rydberg constant or the proton charge radius, and may also be used to probe for hypothetical interactions beyond the standard model. As an introduction to this topic, I will review recent work on the hydrogen and muonic hydrogen atoms, which has led to (at least) partial resolution of the well-known ‘proton radius puzzle’. Then, I will focus on a new player in the field of fundamental metrology, namely the hydrogen molecular ion (H2+, HD+), which is studied both experimentally and theoretically in our team.
