Season 2, Episode 1:
A New Day in the Old Town
Olivia Dunham's car in involved in a traffic collision, but the investigating FBI agent, Amy Jessup, can find no trace of her or the driver of the other car. It's not until Peter, Walter and Charlie arrive an hour later that Olivia turns up -- launching out the front windshield of her car, which had been empty moments earlier. She's in a comatose state and rushed to hospital, where the doctors conclude that she's practically brain-dead and won't wake up. However, she soon does exactly that, first rattling off a phrase in ancient Greek and then waking up proper. She barely remembers anything about what happened, only that she went somewhere, met someone and has an important job to do.
In the meantime, the driver of the vehicle that collided with Olivia's is revealed to be a Shapeshifter: a super-soldier from the alternate universe who can use advanced technology to change its appearance. After failing to kill Olivia in the car accident, the Shapeshifter reports to a safehouse of sorts where a typewriter can be used to communicate with its superiors on the other side: they tell i to interrogate Olivia about what she learned on the other side, then kill her. As this is happening, Broyles is ordered to report to Washington for a hearing in which he must justify the expenses and the continued existence of Fringe Division to the government. The Division is temporary shut down and Peter's credentials are revoked, but he's contacted by Agent Jessup, who is curious about the circumstances of Olivia's disappearance and return. Jessup is introduced to Walter and Astrid, and is inducted into the Fringe team. She and Peter team up to investigate the accident and quickly learn about the Shapeshifter, as well as a tell-tale sign that it leaves on people whose form it has taken (three puncture wounds in the roof of the mouth).
The Shapeshifter tracks Olivia to the hospital and takes the form of a nurse. It discovers that Olivia doesn't remember her time in the alternate universe and attempts to kill her, but Jessup and Peter arrive in the nick of time, having realised that the Shapeshifter -- being a soldier -- will stay on-mission. Jessup shoots it in the back, but it survives and escapes into the basement levels of the hospital. Peter, Jessup and Charlie pursue it through the corridors and rooms, until Charlie manages to corner and kill it in the incinerator room. Its shapechanging device is damaged, but Peter gives it to Broyles so that he can use it and the promise of advanced technology to secure what Fringe Division needs from the government. Peter returns to the hospital to tell Olivia what's happened, and says that the Greek phrase she quoted earlier means "be a better person than your father", and was something his mother used to say. The episode ends with Charlie returning to the incinerator room and the reveal that he's actually the Shapeshifter, who killed the Charlie and took his form. The Shapeshifter disposes of Charlie's body in the incinerator and leaves.