Atomic processes dominate antiproton stopping in matter at nearly all energies of interest. They significantly influence or determine the antiproton annihilation rate at all energies around or below several MeV. This article reviews what is known about these atomic processes. For stopping above about 10 eV the processes are antiproton-electron collisions, effective at medium keV through high MeV energies, and elastic collisions with atoms and adiabatic ionization of atoms, effective from medium eV through low keB energies. For annihilation above about 10 eV is the enhancement of the antiproton annihilation rate due to the antiproton-nucleus coulomb attraction, effective around and below a few tens of MeV. At about 10 eV and below, the atomic rearrangement/annihilation process determines both the stopping and annihilation rates. Although a fair amount of theoretical and some experimental work relevant to these processes exist, there are a number of energy ranges and material types for which experimental data does not exist and for which the theoretical information is not as well grounded or as accurate as desired. Additional experimental and theoretical work is required for accurate prediction of antiproton stopping and annihilation for energies and material relevant to antiproton experimentation and application.