A product of Jokerit's youth system, Teräväinen made his SM-liiga debut on 18 October 2011 at age 17. He quickly established his place in the first team and played 40 games en route to winning the Jarmo Wasama memorial trophy for rookie of the year. During the season, he then entered the 2012 NHL Entry Draft and was ranked as the second best skater out of Europe by the NHL Central Scouting Bureau. He was ultimately selected in the first round, 18th overall, by the Chicago Blackhawks. In his second season in the SM-liiga, Teräväinen played 44 games and scored 31 points. In the following August, he signed a three-year, entry-level contract with the Blackhawks. Teräväinen subsequently participated in Blackhawks' training camp, but returned to Jokerit for the 2013–14 season. After Jokerit star centre Ilari Filppula moved to CSKA Moscow of the KHL, Teräväinen was promoted to become the team's new top-line centerman. However, he started the season relatively slowly, scoring just two points in his first nine games. However, Teräväinen eventually picked up his game and after a successful tournament at the World Junior Championships, went on a 13-game point streak, scoring 5 goals and 18 assists. He ended the season with 44 points in 49 games. He was even named team captain of Jokerit when their captain went down with injury.
Chicago Blackhawks
Teräväinen made his debut for the Blackhawks on 25 March 2014. He scored his first career NHL goal on 16 January 2015 against the Winnipeg Jets. During the 2015 Stanley Cup playoffs, Teräväinen made a large impact in Game 1 of the 2015 Stanley Cup Finals, scoring the tying goal before stripping the puck from the Tampa Bay Lightning's J. T. Brown late in the third period and setting up the eventual game-winning goal scored by Antoine Vermette. He became the fourth-youngest player to ever score a goal in the Stanley Cup Final and the second-youngest to have a multi-point game in the Cup Final since 1990. He won his first Stanley Cup in 2015 with the Blackhawks in his rookie season, scoring ten points in the playoff run.
Carolina Hurricanes
On 15 June 2016, Teräväinen was traded to the Carolina Hurricanes in exchange for the New York Rangers' 2016 second-round draft pick and Chicago's own 2017 third-round pick. Teräväinen scored his first natural hat-trick as a Hurricane on 13 November 2017 in a 5–1 win over the Dallas Stars. On 21 January 2019, Teräväinen signed a 5-year, $27 million extension with the Hurricanes, carrying an annual cap hit of $5.4 million. Teräväinen lead the Hurricanes as their most prolific goal scorer during the 2019 Stanley Cup playoffs helping to the team to reach the NHL Conference Finals after series victories over the defending Stanley Cup champion Washington Capitals and the New York Islanders.
International play
Teräväinen has represented Finland on several youth levels, most notably in the World Junior Championships. In the 2013 tournament, he scored 11 points, placing fourth in the tournament scoring. In the following year, he was named the captain of the team, leading Finland all the way to the final. In the final, Finland defeated Sweden 3–2 in overtime. Teräväinen assisted all three of Finland's goals and was the overall scoring leader of the tournament. After the Carolina Hurricanes failed to make the 2018 playoffs, Teräväinen was named to the Finnish roster to compete at the 2018 IIHF World Championship.
