We overview our recent calculations of scattering cross sections of positronium-antihydrogen collisions. We discuss the cross sections calculated in the vicinity of the four-body resonances of (H) over bar Ps and above the energy threshold for the formation of the antihydrogen positive ions ((H) over bar (+)). In the former energy region where a Rydberg series of resonances dominated by the (H) over bar (+)-e(-) interaction appears, we showa good agreement between the resonant profiles in the cross sections and the resonance energies calculated by the complex coordinate rotationmethod. (H) over bar (+) production cross sections near the threshold energy are reported for the positronium being initially in the (n, l) states with n <= 3, together with all competing elastic/inelastic cross sections. Comparison of our results with the latest continuum distorted wave final state calculation is presented. A qualitative discrepancy concerning the dependence of cross sections on the angular momentum of Ps is indicated.