  pi pi scattering at low energy is sensitive to the structure of the QCD
vacuum. I review the calculations of the pi pi scattering lengths and phases,
and group them in three cathegories: 1. those based on very general theoretical
constraints (like dispersion relations and crossing symmetry) and
phenomenology, 2. those which in addition make explicit use of chiral symmetry,
3. the first-principle ones, done with lattice QCD. I then compare these to the
experimental results. Thanks to recent progress in all these and in the
experimental determination of the scattering lengths we are improving
substantially our knowledge of the QCD vacuum.
