Two-handed
Some weapons are two-handed. You wield them in both hands, which means you cannot wear a shield or engage in two-weapon combat while wielding them.
These weapons are two-handed: tsurugi, dwarvish mattock, two-handed sword, battle-axe, unicorn horn, quarterstaff, and some missile launchers. All other wielded ones are one-handed. Polearms and missiles belong to a separate category.
Monsters (including pets) can wield two-handed weapons if they have the "strong" attribute and are not wearing a shield, in addition to the usual restrictions (must have a weapon attack, no cross-aligned artifacts etc).
Wielding cursed two-handers
Two-handed weapons are infamous for their crippling effect when wielding a cursed one. (Wielding a cursed weapon while wearing a cursed shield has similar drawbacks.) While your hands are welded to a cursed two-hander, you cannot loot or apply containers, cast spells, change your cloak, body armor, or shirt, wear or remove rings, and several other activities. Your god treats this as a major trouble for prayer purposes.
These handicaps make it hard to lift the curse, since your uncursing items will usually be safely in your bag. Gehennom is especially troublesome because you cannot successfully pray. Some people drop holy water on the ground in places you can easily branchport or level teleport to.
Spellcasting monsters, Rodney, and fountain quaffing can curse your items, including your wielded weapon.
