What does Quantum Field Theory in Curved Spacetime Have to Say about the Dark Energy?

The issue of the vacuum energy of quantum fields is briefly reviewed. It is argued that this energy is normally either much too large or much too small to account for the dark energy, However, there are a few proposals in which it would be of the order needed to effect the dynamics of the present day universe. Backreaction models are reviewed, and the question of whether quantum effects can react against a cosmological constant is discussed.