| Year | Date | Historical Events |
| 1956 | May 29 | Keel laid down by the Electric Boat Co., Groton, CT. |
| 1958 | Aug 19 | Launched. |
| 1959 | Nov 10 | Commissioned with CAPT. Edward L. Beach, Jr. in command. |
| 1960 | Feb 15 | Triton began shakedown cruise bound for the South Atlantic, arriving at St. Peter and St. Paul Rocks 9 days later having remained submerged since her departure. |
| | May 10 | Triton completed the first submerged circumnavigation of the earth, after only once surfacing when she transferred a sick sailor to heary cruiser Macon (CA-132) off Montevideo, Uruguary. |
| | May 11 | Triton received the Presidential Unit Citation and CAPT. Beach received the Legion of Merit from President Dwight D. Eisenhower. |
| | Aug 1 | Triton assumed her duties as a radar picket submarine and was deployed to European waters with the 2nd Fleet to participate in NATO exercises. |
| 1961 | Mar 1 | Triton was redesignated SSN-586 due to increased demand for more nuclear powered attack submarines. |
| 1962 | Jun 1 | Triton entered the General Dynamics Co., Groton, CT., for conversion to an attack submarine. |
| 1964 | Mar 1 | Triton completed overhaul and her home port was changed from New London, CT. to Norfolk, VA. |
| | Apr 13 | Triton became the flagship for the Submarine Force, Atlantic Fleet. |
| 1967 | Jun 12 | Triton shifted to her original home port of New London, CT., after the RAY (SSN-653) releived her of flag ship status. |
| 1968 | Oct 1 | Triton underwent preservation and inactivation processes before decommissioning. |
| 1969 | May 3 | Decommissioned. |
| 1986 | Apr 30 | Struck from the Naval Register. |
| 1993 | Aug 1 | The hulk of Ex-Triton was towed by the USS Bolster (ARS-38) to the Puget Sound Naval Shipyard, Bremerton, WA., arriving on 3 September 1993, to await her turn through the Nuclear Powered Ship and Submarine Recycling Program |