The samurai employed various fighting styles and martial arts throughout their history. The specific fighting style or school (ryuha) followed by a samurai often depended on their training lineage, personal preferences, and the time period in which they lived. Here are a few notable martial arts and fighting styles associated with the samurai:

1. Kenjutsu: Kenjutsu refers to the art of Japanese swordsmanship, focusing on the use of the katana and other bladed weapons. It encompasses techniques for both single combat and battlefield engagements.
2. Iaijutsu: Iaijutsu is the art of drawing and quickly striking with the sword in a single fluid motion. It emphasizes the importance of awareness, timing, and precision, allowing a samurai to respond swiftly to sudden confrontations.
3. Jujutsu: Jujutsu encompasses various unarmed combat techniques, including joint locks, throws, strikes, and grappling. It was essential for situations when a samurai found themselves disarmed or facing an opponent at close quarters.
4. Yarijutsu: Yarijutsu refers to the art of spear fighting. Samurai trained in yarijutsu were skilled in using the yari (spear), a versatile weapon effective in both individual duels and on the battlefield.
5. Kyujutsu: Kyujutsu is the art of traditional Japanese archery. Samurai were trained in kyujutsu, developing precision and accuracy in shooting with the yumi (longbow) both on foot and while mounted on horseback.
6. Naginatajutsu: Naginatajutsu involves the use of the naginata, a polearm with a curved blade on the end. Samurai trained in naginatajutsu could effectively employ this weapon for both slashing and thrusting attacks.
7. Sojutsu: Sojutsu refers to the art of spear fighting specifically on horseback. It focused on the techniques and strategies required for cavalry combat, utilizing the yari while mounted.

It's important to note that samurai warriors were not limited to a single style and often had a breadth of training in different martial arts. Additionally, over time, various schools and styles of combat developed and evolved, each with their unique techniques and philosophies. The skills and knowledge of samurai were honed through years of disciplined training and practical experience.