The mystery of cosmological vacuum energy density and the accelerated expansion of the universe

The principles of General Relativity allow for a non-vanishing cosmological constant, which can possibly be interpreted at least partially in terms of quantum-fluctuations of matter fields. Depending on sign and magnitude it can cause accelerated or decelerated expansion at certain stages of cosmic evolution. Recent observations in cosmology seem to indicate that we presently live in an accelerated phase. We recall the history and fundamental issues connected with the cosmological constant and then discuss present evidences for a positive value, which causes the accelerated expansion.