From the medieval period, an indirect process began to replace the direct reduction in bloomeries. This used a blast furnace to make pig iron, which then had to undergo a further process to make forgeable bar iron. Processes for the second stage include fining in a finery forge. In the 13th century  during the High Middle Ages the blast furnace was introduced by China who had been using it since as early as 200 b.c during the Qin dynasty. [https://www.britannica.com/summary/blast-furnace#:~:text=Blast%20furnaces%20were%20used%20in,century%2C%20replacing%20the%20bloomery%20process.] Puddling was also introduced in the Industrial Revolution.
Both processes are now obsolete, and wrought iron is now rarely made. Instead, mild steel is produced from a Bessemer converter or by other means including smelting reduction processes such as the Corex Process.