For centuries after their deaths, the chakras of the sons of the Sage of the Six Paths, Indra and Asura Ōtsutsuki, would continue to be reincarnated into their descendants. During the Warring States Period, their chakras would be reborn into Madara Uchiha and Hashirama Senju, who would continue the brothers' struggle until their own deaths. Prior to Madara's death, Black Zetsu would manipulate him into becoming the first reincarnation to successfully merge Indra's and Asura's chakras, and this would lead to the awakening of theRinnegan.
After Madara's death, the chakra of Indra and Asura would be reborn into Sasuke Uchiha of the Uchiha clan, and Naruto Uzumaki — a descendant of Asura through the Uzumaki clan, respectively. As the first reincarnations to have been born into an era of relative peace, the two would maintain a rather civil rivalry until Sasuke would fall victim to his clan's Curse of Hatred.
The reincarnation cycle will not start again until both of the current reincarnations have passed away; the brothers would not reincarnate until Madara's death, which would occur decades after Hashirama's.
The chakras of Indra and Asura change chakra signatures with each reincarnation. Although Hashirama and Naruto are both Asura's reincarnations, Madara, a sensor type, was able to differentiate their chakras. However, the chakra pathways do not appear to change, or at the very least, contain similarities. Whilst using the Byakugan, Kaguya Ōtsutsuki was able to note that Naruto and Sasuke were the reincarnations of her grandsons. The reincarnations also possess somewhat similar abilities, at least in Indra's case as Madara saw he and Sasuke shared similar abilities, specifically both having the rare Straight Tomoe Sharingan, and correctly speculated they share some connection beyond blood.