  After reviewing the general ideas of quantum cosmology (Wheeler-DeWitt
equation, boundary conditions, interpretation of $\psi$), I discuss how these
ideas can be tested observationally. Observational predictions differ for
different choices of boundary conditions. With tunneling boundary conditions,
$\psi$ favors initial states that lead to inflation, while with Hartle-Hawking
boundary conditions it does not. This difficulty of the Hartle-Hawking wave
function becomes particularly severe if the role of `inflatons' is played by
the moduli fields of superstring theories. In models where the constants of
Nature can take more than one set of values, $\psi$ can also determine the
probability distribution for the constants. This can be done with the aid of
the `principle of mediocrity' which asserts that we are a `typical'
civilization in the ensemble of universes described by $\psi$. The resulting
distribution favors inflation with a very flat potential, thermalization and
baryogenesis at electroweak scale, a non-negligible cosmological constant, and
density fluctuations seeded either by topological defects, or by quantum
fluctuations in models like hybrid inflation (as long as these features are
consistent with the allowed values of the constants).
