There is now a large and increasing body of experimental data and theoretical analyses for reactions that remove a single nucleon from an intermediate-energy beam of neutron- or proton-rich nuclei. In each such measurement, one obtains the inclusive cross section for the population of all bound final states of the mass A-1 reaction residue. These data, from different regions of the nuclear chart, and that involve weakly- and strongly-bound nucleons, are compared with theoretical expectations. These calculations include an approximate treatment of the reaction dynamics and shell-model descriptions of the projectile initial state, the bound final states of the residues, and the single-particle strengths computed from their overlap functions. The results are discussed in the light of recent data, more exclusive tests of the eikonal dynamical description, and calculations that take input from more microscopic nuclear structure models.