In the Underworld, one can be reborn by first getting dipped in the River Lethe to erase their memories and then being born again in the mortal world. If the soul reaches Elysium three times, they can enter the Isles of the Blest.
At Olympus, as Luke is dying, he mutters "Think rebirth...Try for 3 times...Isles of the Blest...." But it is unknown whether he made it there or not.
On the Quest for Thanatos, Frank Zhang and Hazel Levesque shared a blackout. Hazel went to the Underworld with Frank, explaining to him about what happened after she died. In the Fields of Asphodel, Nico di Angelo came to try to find his sister Bianca so that he could bring her soul out of the Underworld but brought Hazel instead. He explained to Hazel that Bianca had been reborn and that he would never see her again.