  We study forward and backward pi-pi scattering within a QCD model based on
the Dyson--Schwinger, Bethe--Salpeter equations truncated to the rainbow-ladder
level. Our microscopic relativistic quark formulation preserves chiral symmetry
and reproduces the observed scattering lengths for total isospin zero, one and
two. At higher energies both scalar and vector meson resonances naturally occur
in the scattering amplitudes. We also report a comparative study with
phenomenological meson-exchange models and find such approaches are reasonable
especially near pi-pi resonances.
