We review recent theoretical efforts to explain observed similarities between electron-atom and positronium(Ps)-atom scattering which also extends to molecular targets. In the range of the projectile velocities above the threshold for Ps ionization (break-up) this similarity can be explained in terms of quasi-free electron scattering and impulse approximation. However, for lower Ps velocities more sophisticated methods should be developed. Our calculations of Ps scattering by heavy noble-gas atoms agree well with experiments at Ps velocities above the Ps ionization threshold. However, in contrast to electron scattering cross sections, at lower velocities they exhibit maxima whereas the experimental cross sections tend to decrease toward lower velocities indicating the same similarity with electron scattering cross section observed above the threshold. Our preliminary results for Ps-N2 scattering confirm experimental observation of a resonance similar to the Πg resonance in electron-N2 scattering.