The squadron's first insignia was approved for use by VF-20 during World War II, and was a "Joker" breaking out of a deck of cards carrying a machine gun.

On 18 September 1970, VA-34 embarked aboard USS John F. Kennedy as part of Carrier Air Wing One for a short at-sea period prior to its scheduled November deployment to the Gulf of Tonkin in the Western Pacific.

However, while en route to the Caribbean for an operational readiness inspection, the ship was ordered to deploy to the Mediterranean after Syria invaded Jordan.

The squadron returned home in March 1971 from this unscheduled deployment, only one year old, but already in possession of the Meritorious Unit Commendation.

Due to the outbreak of the Yom Kippur War, VA-34 and USS John F. Kennedy departed the Norwegian Sea in October 1973 and re-entered the Mediterranean, conducting surveillance operations south of Crete.

As a result of this hostile act, the squadron participated in retaliatory strikes Operation Prairie Fire against Libya by the U.S. 6th Fleet forces in the area.

On the night of 14 April 1986, the squadron conducted a low-level, high-speed attack against targets at the Benina airfield and military barracks in Benghazi, Libya as part of Operation El Dorado Canyon.

The squadron's deployment in 1990 featured integration of night vision goggles and Standoff Land Attack Missile capability into their A-6Es.

During D-Day anniversary ceremonies off the coast of Normandy, President Eisenhower's son John Eisenhower and D-Day veterans embarked on the ship, while Carrier Air Wing Seven conducted a memorial flyover of the Normandy American Cemetery and Memorial at Omaha Beach.

In August 1990, the squadron flew missions from the Red Sea in support of Operation Desert Shield, the buildup of American and Allied forces to counter a threatened invasion of Saudi Arabia by Iraq.

In June 1994, the squadron commemorated the 50th Anniversary of D-Day with a "missing man" formation over Omaha Beach, which was televised worldwide by CNN.

Typical missions included close air support assisting US and United Nations troops on the ground.

Reporting to the 5th Fleet Operating Area, VFA-34 launched strikes over Iraq and Afghanistan, returning home in October 2008.

The wing made only a short deployment aboard Ronald Reagan during exercise RIMPAC between June and August 2014, before the carrier was stationed in Japan.

The wing made its next deployment to the Western Pacific and the Indian Ocean aboard Carl Vinson from 23 January to 23 June 2017.