I assume that by carbon alloys you mean carbon steels.
In that case, remember that steel is made from iron, and that iron is produced in the blast furnace. The product of the blast furnace is called "pig iron", and typically contains 4% +/- of carbon from the coke (a coal product) involved in the process.
To produce steel (usually less than 1% carbon) from pig iron, the excess carbon and other impurities like sulfur and silicon have to be removed. The carbon is removed to the desired level by burning out the excess.
Several processes may be used to do this, but the most modern is the basic oxygen process. In this process, oxygen is blown through the molten iron until the desired carbon content is reached.