A saturation model for the total \gamma \gamma and \gamma^* \gamma^* cross-sections and for the real photon structure function F₂^\gamma (x,Q²) is described. The model is based on a QCD dipole picture of high energy scattering. The two-dipole cross-section is assumed to satisfy the saturation property with the saturation radius taken from the GBW analysis of the \gamma^*p interaction at HERA. The model is combined with the QPM and non-pomeron reggeon contributions and it gives a very good description of the data on the \gamma \gamma total cross-section, on the photon structure function F₂^\gamma (x,Q²) at low x and on the \gamma^* \gamma^* cross-section. Production of heavy quarks in \gamma \gamma collisions is also studied.

PACS numbers: 12.90.+b