The characters in Criminal Minds work for the BAU (Behavioral Analysis Unit) of the FBI.
Their jobs don't actually exist.
Yes, there is a Behavioral Science Unit (BSU) for the Federal Bureau of Investigation and it is sometimes called the Behavioral Analysis Unit.
However, the true reality is that an agent for the BSU does not fly on an airplane to police departments in trouble of trying to complex solve cases, creating profiles, and going after the "unsub". Instead, the BSU is made up of about 8-12 FBI agents. These agents have to personally write a referral to be transferred to that particular department. If an agent is accepted into the BSU, then s/he will literally be in a room reading reports of career criminals and creating profiles based on these long sessions of reading and studying. To be more accurate, a psychologist/psychiatrist will actually be assigned to a police department to help and guide law officials in capturing or interrogating suspects/criminals.
FBI profiles have not worked in the past. In fact, there has been a study conducted that had university students and FBI profilers develop a profile and see the accuracy. There were virtually no differences between the students' and FBI's profiles. However, FBI profilers scored higher in sex-offenders and sex related crimes whereas the students scored higher in the cognitive department.
*Criminal Minds is a televised series on the CBS TV Network Primetime.