This is a difficult question to answer because new materials and alloys are being created all the time, and the material with the highest melting point now could change as new compounds are synthesized. Currently the record-holder is tantalum hafnium carbide (Ta4HfC5), a refractory compound with a melting point of 4488 K (4215 °C, 7619 °F). By mixing together various metals to create alloys, even higher melting points can be achieved. Materials with such exceptional physical properties are sometimes referred to as superalloys.
The chemical element with the highest melting point is carbon, at 4300–4700 K(4027–4427 °C, 7280–8000 °F). The second highest melting point of the chemical elements is tungsten, at 3695 K (3422 °C, 6192 °F), which is why it is used as a filament for light bulbs. Sometimes tungsten is called the element with the highest melting point because carbon does not actually melt under atmospheric pressure, rather it sublimates (transitions directly from a solid to a gas) at 4000 K (3727 °C, 6740 °F).
When very high melting points are desired in a piece of hardware, sometimes ceramics are used. One example is during Project Pluto in the 1950s, when American scientists attempted to create a nuclear-powered ballistic missile with an unshielded, gigawatt-level reactor. The reactor produced such immense heat that a ceramic chassis and components were necessary.
Under extreme pressures, the melting point increases. The Earth’s inner core of iron, for example, has a temperature of approximately 5,000 to 6,000 °C (>9,000 °F), yet it is solid, because the pressure there is about 3 million times greater than on the surface. Conversely, when the pressure is decreased, so does the melting point. On the surface of Mars, pressure is so low that any liquid water would evaporate almost immediately. This is why we have observed evidence of small temporary springs being created on Mars but no permanent bodies of water.