A man is seated in a diner who is revealed as Harold Speck, a traveling salesman. He is joined by a gentleman who asks question which make him uncomfortable. After leaving the diner, Harold is found dead, with his eyelids cut off and clutching a symbol which appears to be a circle with a line through it, which leads to FBI Agents Thomas Mackelway (Aaron Eckhart) and Fran Kulok (Carrie-Anne Moss) being brought in on the case. There appears to be history between Mackelway and Kulok. We learn Kulok has been married but it didn't work out. Before that she was with Mackelway. Flashbacks of Mackelway's recent suspension reveal he received a six-month suspension and psychological evaluation for beating a suspected serial killer, Raymond Starkey (who was in fact a serial killer and went to prison for his crimes). Mackelway receives a series of taunting faxes from someone who may be the killer. Meanwhile, kids go missing and we catch glimpses of a big truck.
As the investigation proceeds, the agents begin to become aware of the possible existence of "Suspect Zero", a "super serial killer" responsible for hundreds of deaths across all 50 states who leaves no evidence behind to link his crimes together. Another body is found in the trunk of a beaten up car, also with his eyelids cut off and cut with the crossed circle mark. The ownership of the car is traced to a halfway house where the manager admits Kulok and Mackelway to a room that was occupied by Benjamin O'Ryan for seven years. The room is filled with obsessive-compulsive sketches of the crossed circle design, a Bible which contains sketches of missing persons, and a book on ritual. Questioning the other occupants of the halfway house, Mackelway is told by one of them the design represents a Zero, not a circle.
The killer sends information to Mackelway which leads him to Benjamin O'Ryan (Ben Kingsley), who believes himself to be a former member of the FBI. The agents must decide if O'Ryan is the key that will allow them to catch Suspect Zero or if he himself is Suspect Zero.
A man kidnaps and begins to rape a girl he followed out of a bar. O'Ryan pulls him out the car window and kills him. When the FBI including Kulok and Mackelway arrive, they find that the body belongs to the serial killer. Starkey, who Mackelway had put away earlier, who had been released from prison.
Evidence uncovered reveals that O'Ryan was part of a secret government experiment (Project Icarus) attempting to cultivate telepathic abilities in individuals (remote viewing) for military purposes. The experiments gave O'Ryan the ability to see the actions of serial killers. These disturbing visions constantly torment O'Ryan and drive him to find the killers and kill them. O'Ryan seeks out Mackelway because Mackelway shares his abilities to some degree. O'Ryan begins to see through Mackelway's eyes, too. Then Mackelway starts seeing through O'Ryan's eyes and Mackelway starts seeing through the serial killers' eyes. Mackelway's boss is not convinced by his theories that O'Ryan is chasing the killer rather than being the killer; Kulok is not sure either.
The actual Suspect Zero is another man who travels around the United States with a refrigerated truck. He targets children, whom he abducts and transports to his ranch to be killed. Mackelway pieces together evidence linking these crimes by recognizing that victims had signs of freezer burns while being transported from their place of kidnap to their resting place. Mackelway chases a suspect truckdriver to a carnival only to find that the child he saw in his vision as 'captured' is free; the truckdriver appears to be his father. Suddenly O'Ryan appears and captures Mackelway. Mackelway wakes tied in front of a mirror as O'Ryan tries to scare him but Mackelway is not frightened. O'Ryan spares him and they drive together while O'Ryan divulges his history with Project Icarus.
Eventually, Mackelway and O'Ryan find Suspect Zero at his ranch. There are many bodies buried in shallow mounds of earth. Chasing him, both vehicles crash off the road. Kulok manages to free the child in the truck trailer, who had been kidnapped from a swing. After a struggle outside, Suspect Zero is killed when Mackelway crushes his skull with a rock. O'Ryan then tries to convince Mackelway to end his suffering by killing him. When Mackelway refuses, O'Ryan pretends to attack him, prompting Kulok to shoot him to defend her partner.

Question: What do Mackleway and Kulok discover in their research?
Answer: The possibility that they may be investigating a super serial killer, responsible for deaths in all the states.
Alternative answer: the symbol is not a circle, it's a zero