Origin: Eloise led the Others when Ben first made contact with them through Richard.
Since Then: Eloise likely left the island soon after Ben's healing in the Temple; she gave birth to Daniel on the mainland. Ben left the island over the years though, and they two may have met regularly. Ben did not, however, appear to know that she was Daniel's mother. By 2007, the two knew each other well, and they worked together to return the Oceanic 6 to the Island. Eloise treated Ben as a subordinate in ordering him around, and she condescendingly dismissed his statements to others as likely lies. Ben considered Jack's private talk with Mrs. Hawking as an honor. Eloise later visited Desmond after Ben shot him, and she laughd in horror at Penny's belief that she was Ben's mother.
Origin: Daniel entered Eloise's camp, demanding to see the island's hydrogen bomb. She took him there, and he vanished.
Since Then: Decades later, Daniel entered the camp again, and Eloise shot him. He revealed he was her son before dying, and his journal confirmed his words. Eloise, pregnant with Daniel at the time, later gave birth to him off the island. Understanding his future and determined to keep him on his path, Eloise consistently pushed her son to succeed at mathematics, dissuading him from pursuing music. Her encouragement worked. Years later, she sent him to the island to his death. In the flash sideways, however, she postponed moving on so they could spend more time together.
Origin: Eloise saw Desmond's name in her son's journal
Since Then: Eloise followed Desmond for some of his life. She was in contact with Brother Campbell, who discouraged Desmond from becoming a monk. Then when Desmond entered Eloise's jewelry shop to buy an engagement ring, she told him not to, telling him his destiny lay on the Island. He bought the ring, but eventually heeded her words. Years later, he remembered Daniel telling him to meet his mother, though Desmond didn't realize he'd already met the woman. He visited her and angrily left. Eloise later visited Desmond in the hospital. In the afterlife, Eloise again tried to convince Desmond to give up his mission. This time, he ignored her completely.
Origin: Jack, a DHARMA Initiative janitor, entered Eloise's camp soon after a man who claimed to be her son.
Since Then: Jack convinced Eloise that he came from the future, and asked her to lead him to the Others' buried bomb. Eloise agreed, alegedly to reset time, but according to Sayid, she really hoped detonating it would wipe out the DHARMA initiative. Richard knocked Eloise out while they were retrieving the bomb, as as far as Eloise knew, he died while trying to detonate its core.
Years later, off-island, Eloise worked to send Jack and the other Oceanic 6 members back to the island. She spoke to Jack alone, explaining the importance of a proxy in returning the island. Her suggestion to give something of hisfather's to Locke's body angered him, but his frustration failed to move Eloise.
Origin: Eli was one of several people in Richard's group of Others
Since Then: Eli was in the Others' hierarchy till she became the latest of several leaders who Richard advised. When a strange man entered the camp and put a gun to Richard, she shot him to save her adviser. The two worked together to retrieve the nuclear bomb they'd once buried, and Richard knocked her out, allegedly to protect her. She left the island soon after, and they may have met again during Richard's frequent off-island trips.
Origin: Both were members of the Others in the early 50s
Since Then: The two rose to levels of authority within the Others' hierarchy, eventually becoming leaders. They also became lovers and conceived a child together. Eloise left the island, perhaps to deliver the child, and Widmore had a second child with another woman. After being banished from the island, he then spend 20 years trying to return, not realizing that Eloise, whose whereabouts he knew, knew how to return all along. Both lived in London for a period, and both eventually conspired to send their son Daniel to the Island.