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If it exists, neutrinoless double-beta decay would be the first known lepton-number violating process, creating matter without antimatter. It would also give us clues to the only observed beyond-the-standard model physics - the fact that neutrinos have mass - as it can only occur if neutrinos are Majorana particles. As this is such an intriguing prospect, there is a wide-ranging international effort to look for the process - but with half-life limits trillions of times longer than the age of the universe, it is a huge challenge. I'll tell you more about the process, and the variety of experimental techniques we're using to look for it, and to ask ourselves the question - how are we living in a universe made of matter?