The most reliable information about crystal structures and their response to changes in pressure and temperature is obtained from single-crystal diffraction experiments. We have developed a methodology to perform single-crystal X-ray diffraction experiments in laser-heated diamond anvil cells and demonstrate that structural refinements and accurate measurements of the thermal equation of state of metals, oxides and silicates from single-crystal intensity data are possible in pressures ranging up to megabars and temperatures of thousands of degrees. A new methodology was applied to solve the in situ high pressure, high temperature structure of iron oxide and study structural variations of iron and aluminum bearing silicate perovskite at conditions of the Earth's lower mantle.