Investigation
The FBI learned of the hijacking while it was in-flight and had an extensive investigation ongoing for many years. The case was called NORJAK, and hundreds of people were interviewed with leads across the nation. The investigation surveyed the entire flight route following Seattle and involved extensive analysis by multiple divisions in the FBI, including handwriting analysis, fingerprint scanning, and psychological profiling. At the time of the five-year anniversary over 800 people had been suspected and all but 24 were eliminated from that pool.
Theory
The FBI did consider that maybe Cooper didn't survive the jump since his parachute couldn't be steered and his attire wasn't suited for a rough landing. This theory was further supported when years later, $5,800 in decaying twenty dollar bills were found in a suitcase in the forest where D.B. Cooper theortically landed. Furthermore, the serial numbers on the bills matched up with the ones used in the ransom. But, there are a couple of suspects who are very popular amongst conspiracy theorists.