The neutron-rich nuclei P-34,P-35,P-36,P-37,P-38 were populated in binary grazing reactions initiated by a beam of S-36 ions at 215 MeV incident on a thin Pb-208 target. The combination of the PRISMA magnetic spectrometer and the CLARA array of escape-suppressed Ge detectors was used to detect gamma rays in coincidence with projectile-like nuclear species. Further evidence to support the observed gamma decay of excited states of the populated phosphorus isotopes is provided by gamma-gamma coincidencemeasurements based on the results of an earlier thick-target deep-inelastic experiment. Level schemes for P-34,P-35,P-36,P-37,P-38 are presented and discussed within the context of state-of-the-art shell-model calculations. In particular, new spin and parity assignments are proposed for a number of excited states of P-36. The evolution with neutron number of the energy difference of the low-lying J(pi) = 3/2(+) and 1/2(+) states in the odd-A isotopes of phosphorus, as well as the relationship to nuclear collectivity, is discussed. The evolution with neutron number of the shell-model wave functions of the first J(pi) = 1/2(,)(+) 3/2(+), and 5/2(+) states of the odd-A phosphorus isotopes and of the first J(pi) = 3(-), 4(-), and 5(-) states of the even-A isotopes is also explored.