Iaijutsu is the art of using the sword (both long and short) from the sheath (saya). Commonly known as Iaido, this art teaches the techniques of defense when attacked or attacking with the katana or wakizai in its saya.
Kenjutsu is the art of using the sword when all ready deployed and usually employs two person forms. A bokuto (wooden sword) is usually used for this type of practice.
Gekken is post modern kendo and involves the use of shinai (bamboo swords) and bogu (armor).
Jōjutsu uses the medium hardwood staff techniques against the sword. It is usually practiced in partner forms like kenjutsu.
The use of light grappling is invovled in muto and yawarajutsu.