Kopitar has spent his entire NHL career with the Kings, has led the team in scoring in all but two seasons and is second in franchise history in points, fourth in goals, and first in assists.

He moved to North America to join the Kings in 2006, one year after he was drafted, and finished fourth in the Calder Memorial Trophy voting for the league's top rookie.

Kopitar's offensive talent was immediately apparent when he joined the Kings, while his defensive style developed in later seasons and he has become recognized for his two-way play, being a finalist for the Selke Trophy four times and winning twice.

Praised as one of the best players in the NHL, Kopitar won the Stanley Cup with the Kings in 2012 and 2014, leading the playoffs in points on both occasions (tied with teammate Dustin Brown in 2012).

Internationally, Kopitar has represented the Slovenian national team in several junior and senior tournaments, as well as at the 2014 Winter Olympics in Sochi.

[2] The Slovenian Ice Hockey League did not have a high enough skill level, so Kopitar decided that if he wanted to improve his career prospects, he would have to leave the country.

[3] He was offered a chance to play in Sweden for Södertälje SK, eventually joining their junior team where he led the League in scoring, with 49 points (28 goals, 21 assists) in 30 games.

[6] At 18 years of age, he declined to move to North America, however, hoping to further his development by continuing to play against professionals in the Elitserien, rather than against major junior players in the WHL.

[9] Kopitar completed his first NHL season third among rookies in scoring, behind Evgeni Malkin and Paul Šťastný, with 20 goals and 41 assists for 61 points.

[17] For the second time in his career, Kopitar won the Bill Libby Memorial Award as the Kings' most valuable player, and led the team in scoring for the third-straight year.

[15] The 2010–11 season saw Kopitar play in his 325th consecutive NHL game, which set a new Kings team record, passing Marcel Dionne on 15 March 2011.

Kopitar finished tied with Kings captain Dustin Brown to lead the team in playoff scoring, with each having 20 points (eight goals, 12 assists) from all 20 games played.

A shortened, 48-game NHL season commenced, Kopitar recorded 10 goals, and 32 assists for 42 points in 47 games to once again lead the Kings in scoring, and was named the team's best defensive player.

He also was a finalist for the Frank J. Selke Trophy as best defensive forward in the NHL for the first time, which was eventually awarded to Patrice Bergeron of the Boston Bruins.

[42] Kopitar returned to form in the 2017–18 season scoring a career-high 35 goals and 57 assists for 92 points in all 82 games played, helping the Kings get back to the playoffs.

In the 2018 playoffs, Kopitar recorded a goal and an assist as the Kings would be swept in the opening round to the Vegas Golden Knights.

[47] On 5 May 2021, towards the end of the pandemic-shortened 2020–21 season, Kopitar recorded his 1,000th career point against the Arizona Coyotes on a Sean Walker goal, becoming the 91st player to reach the mark.

[48] On 14 October 2021, Kopitar scored three goals and two assists against the Vegas Golden Knights, setting a franchise record for most points in a home opening game since Jari Kurri did it back in 1991–92.

He recorded his 700th career assist on a goal by Adrian Kempe in the Kings' final home game of the season on 23 April 2022, a 4–2 win against the Anaheim Ducks.

[52] On 9 January 2023, Kopitar recorded his 1,100th NHL point in a 6–3 win over the Edmonton Oilers with an assist on a Kevin Fiala goal, becoming the third player in Kings history to reach the mark.

[56] On 21 October, in a 4–2 loss to the Boston Bruins, Kopitar passed Dustin Brown as leader of games played in the Kings franchise history.

[59][60] On 20 March 2024, Kopitar recorded his 1,200th NHL point with an assist on a goal scored by Kevin Fiala in a 6–0 win over the Minnesota Wild.

[62] On 30 October 2024, Kopitar recorded his 800th career assist on a goal by Kevin Fiala in a 6–3 win over the Vegas Golden Knights, becoming the 35th player in league history to hit the mark.

At the 2006 World Championship he played for Slovenia at the top level and recorded three goals and nine points in six games, tying for fifth among scoring leaders.

[69] Back in the top division for the 2008 IIHF World Championship, Kopitar appeared in five games and had four points to lead his team, though Slovenia was once again relegated.

[76] Kopitar is known in the NHL as one of the most effective two-way forwards, excelling in both offence and defence, for which he has won the Frank J. Selke Trophy in 2016 and 2018,[77] after being a finalist for the award in both 2014 and 2015.

[82] Matjaž played hockey for HK Acroni Jesenice, winning the league title three times, and was a member of the Yugoslav and Slovenian national teams.

[89][90] Kopitar is renowned in Slovenia due to his hockey exploits, with a government-sponsored website declaring that after he won the Stanley Cup in 2012 he was "the most recognised Slovenian sportsman.