The first reverberatory furnaces were perhaps in the medieval period, and were used for melting bronze for casting bells. They were first applied to smelting metals in the late 17th century. Sir Clement Clerke and his son Talbot built cupolas or reverberatory furnaces in the Avon Gorge below Bristol in about 1678.  In 1687, while obstructed from smelting lead (by litigation), they moved on to copper.  In the following decades, reverberatory furnaces were widely adopted for smelting these metals and also tin.  They had the advantage over older methods that the fuel was mineral coal, not charcoal or white coal (chopped dried wood).
In the 1690s, they (or associates) applied the reverberatory furnace (in this case known as an air furnace) to melting pig iron for foundry purposes. This was used at Coalbrookdale and various other places, but became obsolete  at the end of the 18th century with the introduction of the foundry cupola furnace, which was a kind of small blast furnace, and a quite different species from the reverberatory furnace.
The puddling furnace, introduced by Henry Cort in the 1780s to replace the older finery process, was also a variety of reverberatory furnace.