Abstract: Hydrogen in atomic and molecular form, including the deuterium and tritium isotopes, is key in astrophysics, as well as in stellar and man-made fusion. Hydrogen has become a benchmark system for testing theory at the most fundamental level and for probing physics beyond the Standard Model: are there forces beyond the three included in the Standard Model of physics plus gravity, and are there just 3+1 dimensions. Comparison of laboratory wavelengths of transitions in hydrogen may be compared with the lines observed during the epoch of the early Universe to verify whether fundamental constants of Nature have varied over cosmological time. In recent studies dissociation limits of H2, HD and D2 are measured to 10-digit accuracy. Currently vibrational transitions are being measured via sensitive cavity-enhanced techniques, also for the radio-active HT molecule. In H2 record-high sensitivity is achieved for probing a quadrupole transition in saturation.
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