Oleum is used in the manufacture of many explosives with the notable exception of nitrocellulose.  (In modern manufacturing of nitrocellulose, the HSO concentration is often adjusted using oleum.) The chemical requirements for explosives manufacture often require anhydrous mixtures containing nitric acid and sulfuric acid.  Ordinary commercial grade nitric acid consists of the constant boiling azeotrope of nitric acid and water, and contains 68% nitric acid.  Mixtures of ordinary nitric acid in sulfuric acid therefore contain substantial amounts of water and are unsuitable for processes such as those that occur in the manufacture of trinitrotoluene.
The synthesis of RDX and certain other explosives does not require oleum.
Anhydrous nitric acid, referred to as white fuming nitric acid, can be used to prepare water-free nitration mixtures, and this method is used in laboratory scale operations where the cost of material is not of primary importance.  Fuming nitric acid is hazardous to handle and transport, because it is extremely corrosive and volatile.  For industrial use, such strong nitration mixtures are prepared by mixing oleum with ordinary commercial nitric acid so that the free sulfur trioxide in the oleum consumes the water in the nitric acid.