First of all, there is presently no theory that is able to derive the constants of nature. These constants need to be extracted from experiments. Examples are the coupling constants of the various interactions and the masses of the elementary particles.
Besides that, there is something else we cannot explain: The number three. This should not be some kind of number mysticism, but we cannot explain all sorts of restrictions that are directly connected with the number three.
-Jakob Schwichtenberg, Physics from symmetry