ATO4 compounds are a class of oxides which includes the rare earth element (REE) bearing phosphates and arsenates, REEPO4 and REEAsO4. In this study, we have investigated the isothermal high-pressure and the isobaric high-temperature behaviour of natural samples of xenotime-(Y) (ideally YPO4), chernovite-(Y) (YAsO4) and monazite-(Ce) (CePO4) from the hydrothermal veins cropping out at Mt. Cervandone in the Western Italian Alps. Experimental data based on in situ X-ray diffraction (both single-crystal and powder techniques with conventional or synchrotron radiation) have allowed us to fit the unit-cell volumes and axial thermal and compressional evolution and provide a suite of refined thermo-elastic parameters. A comprehensive analysis of the role played by the crystal chemistry on the thermo-elastic response of these minerals is discussed, along with the description of the main crystal-structural deformation mechanisms for both the zircon (xenotime and chernovite) and monazite (monazite) structural types. Pressure-induced phase transitions of xenotime-(Y) and chernovite-(Y) are discussed and compared with previous literature data, whereas a change in the compressional behaviour of monazite-(Ce) at ∼18 GPa, involving an increase in the coordination number of the REE-hosting A site, is presented and discussed.