Apart from some production of puddled steel, English steel continued to be made by the cementation process, sometimes followed by remelting to produce crucible steel.  These were batch-based processes whose raw material was bar iron, particularly Swedish oregrounds iron.
The problem of mass-producing cheap steel was solved in 1855 by Henry Bessemer, with the introduction of the Bessemer converter at his steelworks in Sheffield, England. (An early converter can still be seen at the city's Kelham Island Museum). In the Bessemer process, molten pig iron from the blast furnace was charged into a large crucible, and then air was blown through the molten iron from below, igniting the dissolved carbon from the coke. As the carbon burned off, the melting point of the mixture increased, but the heat from the burning carbon provided the extra energy needed to keep the mixture molten. After the carbon content in the melt had dropped to the desired level, the air draft was cut off: a typical Bessemer converter could convert a 25-ton batch of pig iron to steel in half an hour.
In the 1860s development of regenerative furnaces and higher temperature refractory lining allowed to melt steel in an open hearth. That was slow and energy intensive, but allowed to better control the chemical makeup of the product and recycle iron scrap.
The acidic refractory lining of Bessemer converters and early open hearths didn't allow to remove phosphorus from steel with lime, which prolonged the life of puddling furnaces in order to utilize phosphorous iron ores abundant in Continental Europe. However in the 1870s Gilchrist–Thomas process was developed, and later basic lining was adopted for the open hearths as well.
Finally, the basic oxygen process was introduced at the Voest-Alpine works in 1952; a modification of the basic Bessemer process, it lances oxygen from above the steel (instead of bubbling air from below), reducing the amount of nitrogen uptake into the steel. The basic oxygen process is used in all modern steelworks; the last Bessemer converter in the U.S. was retired in 1968. Furthermore, the last three decades have seen a massive increase in the mini-mill business, where scrap steel only is melted with an electric arc furnace. These mills only produced bar products at first, but have since expanded into flat and heavy products, once the exclusive domain of the integrated steelworks.
Until these 19th-century developments, steel was an expensive commodity and only used for a limited number of purposes where a particularly hard or flexible metal was needed, as in the cutting edges of tools and springs.  The widespread availability of inexpensive steel powered the Second Industrial Revolution and modern society as we know it.  Mild steel ultimately replaced wrought iron for almost all purposes, and wrought iron is no longer commercially produced.  With minor exceptions, alloy steels only began to be made in the late 19th century.  Stainless steel was developed on the eve of World War I and was not widely used until the 1920s.