Kenjutsu is the Japanese art of the practical "battlefield" application of the Japanese sword. Like epee in Western fencing and unlike kendo, the curriculum is generally not constrained to particular body parts. Unlike kendo and Western fencing, it is not typically practiced through free-sparring. There are some schools that practice with contact but it is usually in a strongly controlled way. Rather, most practice is done through set forms (kata) and cutting exercises (tameshigiri). Keeping your students alive is generally a Good Thing when establishing the school, or ryu.
There used to be hundreds of different kenjutsu ryu. Now, just a handful survives. Some examples: