Steel's hardness is determined by its carbon content as well as the tempering process, and steel makers also use the word "temper" to refer to its percentage of carbon. The tempering process for steel differs depending on the use which the steel will have. For example, when making tools, the steel is hammered lightly as it cools, whereas when making springs, the steel is cooled quickly by placing it in oil.
Precipitation-hardened alloys such as aluminum, magnesium, nickel, and titanium, must first go in solution before you can temper them. This allows the impurities to become fixed in their locations so that the particles are spread evenly throughout the metal, giving it strength. This process is sometimes also referred to as "aging."
Whereas in manufacturing, the tempering process can be gauged by the color of steel, in blacksmithing, the temperatures used are sometimes too low for this. In lieu of color, blacksmiths rely on the length of time the steel has been heated to make decisions. Sometimes they also use the color of the oxide film that forms on the metal in the presence of air, which can be anywhere from a pale straw color to a deep blue color.
Annealing is the type of tempering which makes metal softer by a slow cooling. This can be useful if the metal is going to be machined or worked on a lathe, where its ductility (ability to deform under stress) is important.