[5] In the high school tournament of the 2002 Korean National Sports Festival, he played for Jeju's provincial team, and won the title.

[2] During the first three years in Pohang, he failed to make any appearances for club's senior team due to becoming an understudy to first-choice goalkeeper Kim Byung-ji.

[7] Because of Kim's existence, Jung had thoughts of performing military duties, but was talked out of it by reserve team coach Park Tae-ha, who told he would get his chance.

[7] Jung started to compete with Shin Hwa-yong for the role as a starter since the 2006 season after Kim left Pohang.

He left a memorable game by changing his role to an outfield player just before the penalty shoot-out in the 2009 K League Championship.

[17] While contributing to winning the 2010 AFC Champions League title,[18] he played all twelve matches from the group stage to the final and kept five clean sheets.

On 28 January 2011, it was announced that Jung had joined Suwon Samsung Bluewings on a five-year deal for undisclosed fee.

However, Al-Sadd striker Mamadou Niang suddenly intercepted the ball in front of Jung and scored the discourteous goal.

After the end of the 2012 season, he was nominated for the K League FANtastic Player award, but lost to Dejan Damjanović.

[27] In the middle of the season, some British clubs including Queens Park Rangers, Fulham and Celtic were interested in Jung,[28] but he failed to leave for Europe.

In the 2015 season, he had difficulty in playing all of Suwon's matches due to his knee injury,[29] and second-choice goalkeeper No Dong-geon got a considerable number of opportunities.

After suffering a knee injury in mid–September 2016, Jung returned to the field in an Emperor's Cup match against Urawa Red Diamonds on 12 November.

He blocked Zlatan Ljubijankić's shot in the penalty shoot-out after a 3–3 draw with Urawa, helping Kawasaki advance to the next round.

The defender Tatsuki Nara wore gloves for the rest of the time after Jung was sent off for a foul on opponent forward Andrew Nabbout in the 70th minute, because Kawasaki already used three substitutes.

[45] After a friendly against Paris Saint-Germain on 20 July 2022, Jung was evaluated as a masterclass goalkeeper by opponents' website, although his team lost 2–1.

[60] Nevertheless, he, along with Lee Chung-yong and Park Ji-sung, were voted South Korea's MVP in the World Cup by fans.

[65] South Korea met Great Britain in the quarter-finals after Jung conceded just one goal in three group matches.

South Korea encountered crisis by giving two penalty chances to Aaron Ramsey in the first half, but Jung blocked one of the two.

[67] Lee conceded three goals in the semi-final defeat to Brazil while Jung was absent from the team due to a shoulder injury.

He conceded two goals in five matches during the tournament, playing a vital role in Korean football's first-ever Olympic medal.

[72] Jung saved nine of Russia's ten shots on target in South Korea's first match, gaining respect from the press.

[82][83] Jung has a tattoo on his left wrist that said: "1 means my pride as a goalkeeper and my sense of responsibility as a keeper.