Leslie was the person who comforted Bruce Wayne (Batman) after his parents were murdered. She seems to have had some level of romantic relationship with Bruce's butler Alfred Pennyworth.
Leslie Thompkins was the creation of writer Dennis O'Neil and artist Dick Giordano first appearing in Detective Comics #457, dated March 1976.
Modern Age / New Earth
Leslie is also a friend and confidante of Catwoman. She is disapproves of Batman endangering teenagers by training them to be superheroes.
New 52 / Earth One
Leslie character is pretty much the same as her New Earth version.
Major Story Arc
Modern Age / New Earth
As a result, before Infinite Crisis changed some past events in the DC universe, Leslie was also responsible for the death of Stephanie Brown (Spoiler, and briefly the fourth Robin). When Stephanie was mortally injured by Black Mask during the War Games storyline, Leslie deliberately withheld medication that could have saved Stephanie's life, in hopes that her death would finally convince Batman that superhero life was too dangerous for teenagers.
Many comics readers objected to this storyline, feeling that it was completely out of character. In any case, the Infinite Crisis storyline retroactively erased Leslie letting Stephanie die. Instead, it was revealed that Leslie had faked Stephanie's death in order to get her out of the superhero business and to give her time to heal without worrying about Black Mask.
After Battle for the Cowl she has started a new clinic and has Mortimer Drake aka as The Cavalier as a personal Bodyguard. Tim Drake is still holding a grudge against Leslie.
During the Skeleton Keys arc, James Gordon Jr. volunteers at Leslie's clinic. Gordon still doesn't know what to think about his son until James informs him about his volunteer work at Dr. Thompkins' clinic.
It seems everyone was right about James Jr. even though Gordon tried to give him the benefit of the doubt. Gordon immediately goes to the clinic and finds Dr. Thompkins. Gordon confronts Leslie by demanding to know where his son is. Leslie informs Gordon that his son is a model volunteer because anything she asks him to do, he "happily" does. Over time, Leslie has given James Jr. more responsibilities like making "nutrition runs" for newborn babies who come from poor families. Gordon doesn't want to panic Leslie by telling her what he had found at his apartment so he humbly asks her to call him the moment James comes in for his shift. Leslie agrees to Gordon's request and she tries to calm his worries by showing him James' office.
Leslie flips on the lights in James' office and gives Gordon a tour. As Leslie professes how great James is, Gordon on the other hand, can't believe that Leslie would be so naive to willingly put her full trust in someone like James. Gordon peers around the office and finds a vile of James' medicine. The medicine is called Diaxemene which is designed to release a chemical in the brain so the patient can feel empathy. Gordon takes a pill from the vile, thanks Leslie for the tour and makes his way to Barbara's place at Kord Tower.
Batman: The Animated Series
Leslie Thompkins was a doctor who went to medical school with Thomas Wayne and Matthew Thorne. The three were best friends. After Thomas and Martha Wayne were shot in Park Row, Dr. Thompkins consoled the young son of her friends.
Bruce and Leslie became close friends over the years. In fact, Leslie was one of the few people that Bruce trusted with the knowledge of his secret identity as Batman. In fact, she became indirectly involved in Batman's adventures on a few occasions. Examples include, when she was kidnapped by Rupert Thorne's men and forced to render medical aide against her will and when Batman was blinded in an accident and she treated him. Leslie also managed the Thomas Wayne Memorial Clinic, a free clinic for the poor which Bruce had setup in memory of his father. She was also the one Batman turned to when he needed medical attention that went beyond the abilities of himself or Alfred. She is voiced by Diana Muldaur.
Leslie, played by Morena Baccarin, made her live action debut in FOX's television drama Gotham, set just after the Wayne murders. This younger version of the character makes her debut n the episode "Rougue's Gallery" as a doctor operating in Arkham Asylum's female ward. There she befriends the young James Gordon, working security at the Asylum after disciplinary action from the GCPD.
She continues her friendship with Gordon even after he returns to police duty, and the two soon begin a romantic relationship.
Leslie's Medical Clinic can be seen toward the north-east corner of the game map.