The pressure-and temperature-induced phase transitions in FeS have been explored by X-ray diffraction measurements made on single-crystal samples. It is found that the room temperature and pressure structure, troilite (a close relative of the NiAs-type structure), with space group P(~2c and a unit cell of a = v/3A and c ---2C (where A and C refer to an NiAs-type structure and are approximately 3.4 and 5.9A, respectively), transforms at 420 K and ambient pressure, and at 298 K and 3.4 GPa to an MnP-type structure. This structure has space group Pnma and the orthohexagonal unit-cell dimensions a = C, b = ,4 and c -v/3A. For FeS, the deviation of its unit cell from these ideal dimensions is small, and although the transformation results in a triply twinned crystal, the profiles of reflections containing contributions from multiple-twin domains are broadened but not split. A comparison of data from structure refinements adjacent to these transitions shows that, in both cases, the MnP-type phase has an increased distortion of the S atoms from planarity, a less distorted FeS 6 polyhedron, and longer Fe-Fe bonds. The differences in distortion between the structures suggests that their stabilities may depend upon the relative energy contributions from the distorted polyhedron and the Fe-Fe bond. Further increases in temperature produce a second-order transition to an NiAs-type structure, space group P63/mmc, whereas higher pressures cause an increasing sinusoidal distortion of the essentially h.c.p. S atoms. At 298 K and 6.7 GPa another transition takes place to an unknown structure. This transition is accompanied by a 9% volume change and a large decrease in C/A.