Using multi-anvil high-pressure devices and synchrotron radiation, X-ray in situ observations of HfO2, under high pressure and high temperature have been performed to investigate its phase relations and compression behavior. An orthorhombic phase (orthoI) is stable from 4 to 14.5 GPa below 1250 degrees -1400 degreesC and transforms to a tetragonal phase, which is one of the high-temperature forms of HfO2, above these temperatures. Another orthorhombic phase (orthoII) with a cotunnite-type structure appears above 14.5 GPa, OrthoII is stable up to 1800 degreesC at 21 GPa, OrthoII is quenchable to ambient conditions, The orthoI-to-orthoII transition is accompanied by similar to8 vol% decrease, The bulk moduli of orthoI and orthoII at room temperature are 220 and 312 GPa, respectively. This low compressibility of orthoII indicates that it is a potential candidate for very hard materials.