Abstract
After a short history of the 
-term it is explained why the (effective) cosmological constant is expected to obtain contributions from short-distance physics, corresponding to an energy scale of at least 100 GeV. The actual tiny value of the cosmological constant in any natural scale of units represents, therefore, one of the deepest mysteries of present-day fundamental physics. We also briefly discuss recent astronomical evidence for a cosmologically significant vacuum energy density causing an accelerating expansion of the universe. This arises mainly from the Hubble diagram of type Ia supernovae and from the observed temperature fluctuations of the cosmic microwave background radiation. If this should become an established fact, we are also confronted with a disturbing cosmic coincidence problem.