She is a mystery to me. Now she left the island for some unknown reason relinquishing her leadership.
But now that she is off the island, there are some questions that need to be asked.
1. Why did she need Desmond to go to the island and press the button? Was it because he was in love with Penny and Penny is Widmore's daughter? 2. Why is she helping Oceanic Six get back?
a. From many of the opinions here, Christian is working for Un-Locke. And so he tells Locke to meet Eloise Hawking. So, is Eloise working for Un-Locke? Maybe that's the reason why she makes them take Locke's body as Un-Locke cannot become Un-Locke unless he has the body. b. She gives Jack the letter from Locke. Who gives her the letter? And why is the letter important even now that Jack is convinced he has to go back? c. From Eloise's encounter with Penny in "The Incident", Desmond getting shot is not something that has happened yet? What is the time till she knows what is going to happen?
Many more questions could be added to this. :)