The neutron-rich nuclei 34,35,36,37,38 P were populated in binary grazing reactions initiated by a beam of 36 S ions at 215 MeV incident on a thin 208 Pb target. The combination of the PRISMA magnetic spectrometer and the CLARA array of escape-suppressed Ge detectors was used to detect γ rays in coincidence with projectile-like nuclear species. Further evidence to support the observed γ decay of excited states of the populated phosphorus isotopes is provided by γ -γ coincidence measurements based on the results of an earlier thick-target deep-inelastic experiment. Level schemes for 34,35,36,37,38 P 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 36 P. The evolution with neutron number of the energy difference of the low-lying J π = 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 π = 1/2 + , 3/2 + , and 5/2 + states of the odd-A phosphorus isotopes and of the first J π = 3 − , 4 − , and 5 − states of the even-A isotopes is also explored.