I give an overview of experimental and theoretical results for antiproton and antihydrogen scattering with atoms and molecules (in particular H, He). At low energies (less than or similar to 1 keV) there are practically no experimental data available. Instead I compare the results from different theoretical calculations, of various degrees of sophistication. At energies up to a few tens of eV, I focus on simple approximations that give reasonably accurate results, as these allow quick estimates of collision rates without embarking on a research project. This article is part of the Theo Murphy meeting issue 'Antiproton physics in the ELENA era'.