The noncommutative localization is a common term for several kinds of localization which occur in noncommutative ring theory and in particular the (left or right) Ore localization, Gabriel localization? and Cohn universal localization of rings and of their associated categories of modules?. The language of torsion theories? was originally developed also in this context, but in fact it can pertain to a more general situation than to the categories of modules over rings.