Dark Energy in Extra Dimensions and String Theory: Consistency Conditions

The smallness of the cosmological constant is one of the basic problems in particle physics and cosmology. Various attempts have been made to explain this mystery, but no satisfactory solution has been found yet. The appearance of extra dimensions in the framework of brane world systems seems to provide some new ideas to address this problem from a different point of view. We shall discuss some of these new approaches and see whether or not they lead to an improvement of the situation. We shall conclude that we are still far from a solution of the problem.