The progress of Particle Physics is closely linked to the progress in the understanding of the fundamental constants, like the finestructure constant, the mass of the electron or nucleon, or the electroweak mixing angle. The relation between the 18 fundamental constants of the Standard Model and the elementary units used in other fields like quantum optics or solid state physics is far from trivial and will be discussed. Relations between the various constants might exist, providing signals for the physics beyond the Standard Model. Recent observations in astrophysics indicate a slight time variation of the finestructure constant. If true, it has profound implications for many particle and nuclear physics phenomena. In particular the nuclear mass scale should change in time, a phenomenon that could be observed in the laboratory using advanced methods of quantum optics.