The fourth edition of the CATMIN conference was held from May 20 to 23, 2025, at the Universidad de Granada, in the beautiful city of Granada in Spain. The Cold Atom Molecule Interactions – CATMIN conference is a biannual event, whose previous editions were held in Paris (France), Waterloo (Canada), and London (UK). CATMIN IV covered all areas of Rydberg physics from quantum sensing, computing and simulation to precision spectroscopy and cold chemistry.