Origin: Ben kidnapped Alex when Widmore ordered him to kill her mother.
Since Then: Ben raised Alex as his daughter. He protected her excessively, fearing her becoming pregnant. She rebelled and said she hated him. Keamy held her hostage, and when Ben called his bluff, Keamy shot her. The guilt haunted Ben for the rest of his life and beyond.
Since Then: Isolation following Alex's kidnapping drove Danielle insane. When she trapped Sayid, she interrogated him about Alex's whereabouts. She later kidnapped Aaron, hoping to exchange him for Alex. Shortly after she helped the survivors defend themselves from an Other attack, Alex and Danielle finally reunited. They both died shortly afterward.
Since Then: Karl was locked in a cage by Ben in an attempt to keep him away from Ben's daughter, Alex. Alex was determined to prevent this from happening, and she later struck up a deal with Kate and Sawyer to help her free Karl in exchange for a boat to take them off Hydra Island. They broke into Room 23, where Karl was being forced to watch various images while listening to loud techno music. Alex was prevented from leaving the smaller island by Juliet, and settled for Karl escaping with Kate and Sawyer. Ben later revealed to Alex that the reason why he wanted to keep Karl away from her was to prevent her from getting pregnant, thus causing her to die. Alex and Karl were later reunited at the radio tower. Karl was with Alex and Danielle when he was shot and killed. Later, Alex was shot in the head by Keamy during a stand-off with Ben at the Barracks.