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This thesis presents the experimental investigation of structure and melting of three important materials under extreme conditions of high pressure and high temperature. The melting points of elements and compounds are of fundamental importance for the study of planetary interiors and for fundamental and applied physics. The high pressure apparatus used in this thesis is the diamond anvil cell, which has been used to reach pressures of up to 137 GPa and temperatures up to 6000-7000 K via laser-heating techniques. The melting point has been determined at high pressure by the first onset of liquid scattering in X-ray diffraction patterns that are collected in situ. At temperatures towards the melting point, important information on the crystalline state of these materials has been extracted. The polymorphism of Sn has been studied into the megabar range (P > 100 GPa) at room temperature. The equation of state of Sn has been determined up to 137 GPa. A previously unreported structural transformation occurs at 32 GPa into a body centered orthorhombic structure (spacegroup Immm). Coexistence of this polymorph with a body centered cubic structure (spacegroup: Im-3m) is observed over a wide pressure range. These new findings for this important element are reported within. The melting relations of Sn have been determined to beyond 1 megabar in pressure and reveal a dip in the melt slope followed by a sudden sharp rise between 40 and 70 GPa. High temperature experiments using resistive-heating and laser-heating in the diamond anvil cell reveal the observation of multiple X-ray diffraction signatures at high temperatures. The results are discussed and overlap with the discoveries from the room temperature investigation of Sn. TaC and MgO are two important refractory materials and have also been investigated using laser-heated diamond anvil cell techniques combined with in situ synchrotron X-ray diffraction. TaC has the highest ambient melting temperature of any binary compound. MgO constitutes approximately 37 % of the Earth’s lower mantle and the melting temperature as a function of pressure can provide us with information on the melting behaviour, phase relations and rheology of the Earth’s lower mantle. The results and their impact on current high pressure research are discussed.