Quantum Cosmology and the Constants of Nature

In models where the constants of Nature can take more than one set of values, the cosmological wave function $\psi$ describes an ensemble of universes with different values of the constants. The probability distribution for the constants can be determined with the aid of the `principle of mediocrity' which asserts that we are a `typical' civilization in this ensemble. I discuss the implications of this approach for inflationary scenarios, the origin of density fluctuations, and the cosmological constant.