Hydrogen direct reduction is one of the technological process solutions for making steel, explored in the framework of reducing GHG emissions from the steel sector (Net-Zero steel). However, there are many other solutions, which have been explored since the 1980s or earlier. The present paper starts by comparing all these different options in terms of 3 criteria: energy needs, GHG emissions and total production cost of steel. The extensive simulations carried out as part of the ULCOS Program, which are still fully valid, indeed show that, while energy is always rather close to the efficient integrated steel mill benchmark (within 15–20%), there are a series of solutions for significantly cutting GHG emissions, some of which even leading to negative emissions. Two families of solutions can usefully be compared with each other, as they are both based on the use of electricity: hydrogen direct reduction, from green hydrogen generated from green electricity, and electrolysis of iron ore, such as the ΣIDERWIN process, also based on zero-carbon electricity. They are quite close with regards to the 3 above criteria, with a slight advantage for electrolysis. Focusing now on hydrogen steelmaking, the process developed over the last 70 years: the H-Iron process was first explored in 1957 at laboratory level, then it was followed by an industrial first plant in the late 1980s, which did not fully deliver (CIRCORED); a sub-project within ULCOS (2000s) followed, then some projects in Germany and Austria (SALCOS, SUSTEEL, MATOR, based on direct reduction and smelting reduction, 2010s) and then, very recently, occurred an explosion of projects and announcements of industrial ventures, both for generating hydrogen and for producing DRI, located in Europe, Russia and China. Broader questions are then tackled: how much hydrogen will be called upon, compared to today and future needs, regarding in particular H2-e-mobility; carbon footprint and costs; maturity of the various processes; and geopolitical issues, such as possible locations of H2-generation and H2-steel production.