  Although most fundamental laws are invariant under time reversal, experience
exhibits the presence of irreversible phenomena -- the arrows of time. Their
origin lies in cosmology, and I argue that only quantum cosmology can provide
the appropriate formal framework. After briefly reviewing the formalism, I
discuss how a simple and natural boundary condition can lead to the observed
arrows of time. This yields at the same time interesting consequences for black
holes.

General Relativity and Quantum Cosmology