He played college football for the UCLA Bruins, where he was the school's career leader in both total offense and touchdown passes.

He was selected by the Green Bay Packers in the fifth round of the 2015 NFL draft, and started nine games for them in 2017, following a collarbone injury to Aaron Rodgers.

[6] Hundley also helped UCLA defeat the USC Trojans 38–28 for the first time since 2006, passing for 234 yards including 1 touchdown.

The team beat USC, by a score of 35–14, marking consecutive wins over their crosstown rivals for the first time in over a decade.

[10] UCLA won the Sun Bowl, 42–12, over Virginia Tech with Hundley being named the game's co-most valuable player with teammate Jordan Zumwalt.

[13] Wary of the criticism of his passing skills, Hundley attempted to impress the pro scouts by running the ball less to begin the 2014 season.

[15][16][17] Through 32 career games, he was sacked 107 times, the highest among active Football Bowl Subdivision quarterbacks.

[9][22] After the season, Hundley entered the 2015 NFL draft and was chosen much later than expected, in the fifth round with the 147th overall pick by the Green Bay Packers.

Hundley's success in the preseason and his off-the-field maturity eventually led to him being named the Packers' second-string quarterback after Tolzien's departure to the Indianapolis Colts in March 2016.

[31] On October 15, 2017, during the first quarter of the Week 6 game against the Minnesota Vikings, Rodgers suffered a broken collarbone on a hit made by Anthony Barr.

[32] Hundley then entered the game, completing 18-of-33 passes for 157 yards, one touchdown, and three interceptions, as the Packers lost by a score of 23–10.

After the game, head coach Mike McCarthy stated that Hundley would take over as the starter due to Rodgers's broken collarbone.

[33] In his first career start against the New Orleans Saints, Hundley recorded 12 completions on 25 attempts for just 87 yards, no touchdowns, an interception, and ended with a passer rating under 40 for the second consecutive week.

[35] He continued this improvement into Week 10, with 18-of-25 completions, passing for 212 yards, no interceptions, and his first career 100+ passer rating in a win over the Chicago Bears.

[36] Hundley had 200+ passing yards for his third consecutive outing in Week 11, but committed three interceptions with no touchdowns, during the team's shutout loss to the Baltimore Ravens.

[37] In a Week 12 loss to the Pittsburgh Steelers, Hundley improved with three touchdowns, finishing the day with a 134 passer rating for his efforts.

[43] On August 29, 2018, Hundley was traded to the Seattle Seahawks for a sixth round pick in the 2019 NFL draft (which was used on running back Dexter Williams.