Do we live in the Best of all possible Worlds? The fine-tuning of the constants of Nature

Our existence depends on a variety of constants which appear to be extremely fine-tuned to allow for the existence of life as we know it. These include the number of spatial dimensions, the strengths of the forces, the masses of the particles, the composition of the Universe and others. On the occasion of the 300^th anniversary of the death of G.W. Leibniz we discuss the question of whether we live in the "Best of all possible Worlds". The hypothesis of a multiverse could explain the mysterious fine tuning of so many fundamental quantities. Anthropic arguments are critically reviewed.