The ninja clans in Naruto are a major part of its story. Almost every important character in the series comes from one prominent clan or another. Among the most critical clans is the Senju clan. They are the direct descendants of the Sage of Six Paths, who spread chakra throughout the world. They were one of the strongest clans during the Warring States Period, and co-founded the Hidden Leaf Village, alongside the Uchiha clan. However, despite their importance, the clan seems to have disappeared by the start of Naruto.
It's surprising that such a prominent and powerful clan would vanish without a trace. The only living descendent of the Senju clan who's shown in Naruto is Tsunade, the granddaughter of Hashirama Senju. One would think that such an important clan would have dozens of members appear throughout the story. However, no known living villagers even bear the last name. Unlike the Uchiha and Uzumaki clans, which were massacred, the Senju clan is never stated to have been wiped out. The series never gives a clear explanation as to why the Senju clan is gone, but there are some plausible theories.
Constant Wars Destroyed the Senju Clan
By the time the series begins, the world of Naruto had already endured three Shinobi World Wars within a relatively short amount of time. These were massive conflicts that involved all the hidden villages and led to the deaths of thousands of ninjas. As the founders of the Hidden Leaf Village and one of the strongest clans, the Senju would have been expected to take part in this war.
It is known that multiple members of the Senju clan fought and died in these Shinobi World Wars. The first and second Hokages, Harishrama Senju and his brother Tobirama, both fought and perished in the First Shinobi World War. Tsunade took part in the Second Shinobi World War as well. Her little brother Nawaki died in this war. In fact, a known member of the Senju clan has been a part of nearly every Shinobi World War and died in the conflict.
It's possible that the Senju clan lost the majority of its members during these wars. They would have been pushed to take on the most dangerous and important missions because of their clan's renowned strength. The Senju clan also developed the philosophy of the Will of Fire, which prioritized the safety of the village above all else. This mindset would have emboldened many members of the clan to sacrifice themselves for their comrades and the protection of their home.
The Senju Clan May Have Disbanded for Their Safety
It isn't uncommon for powerful clans to be targeted for kidnappings and assassination. Many villages and clans fear powerful ninjas and covet their secret jutsu. There are multiple instances of coordinated efforts to kidnap children with strong kekkei genkai or massacre clans that are known for their strength. For example, Orochimaru spent multiple years attempting to take over the bodies of Sasuke and Itachi Uchiha so that he could have their Sharingan. The Hyuga clan's branch family is branded with a curse seal that makes sure their Byakugan is locked away upon death. Hinata Hyuga was almost kidnapped as a child by a Cloud ninja. The Uzumaki clan and their homeland were wiped out because of their skill in sealing jutsu.
The world would be a dangerous place for members of the Senju clan, who are naturally strong shinobi because of their relation to the Sage of Six Paths. Harisharama is the only known member of the Senju clan to manifest Wood Release, but other villages might have wanted to kidnap his descendants so they could replicate his abilities. Having the last name Senju would put a big target on any clan member's back. The clan could have decided to disband to avoid being targeted by their enemies. The surviving members would have gotten rid of their last names and scattered throughout the village. It's worth noting that both Tsunade and her brother are never referred to by their last names. Despite being the grandchildren of the most famous Senju, they don't carry the name, which supports the theory that its members went into hiding. In fact, Jiraiya and Naruto had to hunt Tsunade down in order to bring her back so she could become the Fifth Hokage, and while she had plenty of reasons to disassociate herself from the village after the war, there's a strong possibility she may have been hiding.
The Senju Clan May Have Merged with Leaf Village
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The simplest answer might also be the correct one. The Senju clan were the co-founders of the Leaf Village and were loved by almost the entire village. They valued the village above all and were heavily invested in its development. The Senju clan could have simply married into the other clans and taken their spouses' last names, completely assimilating into the village until their seeming disappearance.
There is some evidence to support this theory. When Orochimaru was attempting to infuse Hashirama's cells into children so that they would gain Wood Release, Yamato was the only survivor out of sixty children. It's possible that he was the only survivor because he was distantly related to the Senju clan without even knowing it. It's also been revealed in Boruto that Moegi Kazamatsuri, Konohamaru's former teammate, can use Wood Release as well.
There is a strong possibility that both the Leaf Village and the Land of Fire are filled with secret Senju Clan members who are completely unaware of their heritage. Through intermarrying with the villagers, the Senju clan could have massively increased the strength of the Leaf Village with their powerful chakra. This may be why the Leaf Village produces such exceptionally strong shinobi compared to the other villages.