Russell began karting in 2006 and progressed through to the cadet class by 2009, becoming MSA British champion and British Open champion. In 2010 he moved to the Rotax Mini Max category where he became Super One British champion, Formula Kart Stars British champion and also won the Kartmasters British Grand Prix. Russell graduated to the KF3 class in 2011, winning the SKUSA Supernationals title and becoming CIK-FIA European Champion, a title he successfully defended in 2012. In his final year of karting in 2013, Russell finished 19th in the KF1 CIK-FIA World Championship.

In 2014, Russell made his single-seater debut, racing in the Formula Renault 2.0 Alps championship. He originally signed to race for Prema Powerteam, before making a last-minute switch to Koiranen GP. Despite missing a round through illness, he finished fourth in the championship, taking a single podium finish at the Red Bull Ring.

In 2014, Russell also competed in the BRDC Formula 4 Championship with defending champions Lanan Racing. He entered the final race of the season at Snetterton in a four-way title battle with teammate Arjun Maini and the HHC Motorsport pairing of Sennan Fielding and Raoul Hyman. After starting from pole position, Russell won the race, his fifth of the season, to clinch the title by just three points from Maini.

As a prize for winning the BRDC Formula 4 championship, Russell tested a GP3 car with Arden Motorsport at the Yas Marina Circuit in Abu Dhabi. In December 2014, Russell became the youngest-ever winner of the prestigious McLaren Autosport BRDC Award, beating fellow finalists Alexander Albon, Ben Barnicoat, Sennan Fielding, Seb Morris and Harrison Scott to earn himself a £100,000 cash prize, British Racing Drivers’ Club membership and a Formula One test with McLaren.

In February 2015, Russell was announced as one of the twelve drivers selected to join the British Racing Drivers’ Club SuperStars programme, the youngest-ever recruit to the scheme.

Russell graduated to Formula Three in 2015, racing in the FIA European Formula 3 Championship with Carlin. He took his first race victory in the opening round of the season at Silverstone, finishing ahead of fellow debutant Charles Leclerc and Antonio Giovinazzi in the second race of the weekend. He took a further two podium places at Spa-Francorchamps and the Norisring to finish sixth in the championship. He also finished as runner-up to Leclerc in the rookie championship standings.

In September 2015, Russell took part in the Masters of Formula 3 non-championship event held at Zandvoort. After finishing fourth in the qualification race, he went on to finish second behind teammate Antonio Giovinazzi in the main race. Russell was also scheduled to compete in the Macau Grand Prix with Carlin, but was replaced by Japanese Euroformula Open Championship driver Yu Kanamaru shortly before the event.

Russell signed with ART Grand Prix for the 2017 GP3 Series season. He had previously driven for the team at the post-season test at Yas Marina in November 2016.

In early 2017, Russell joined Mercedes-AMG Petronas Motorsport as a part of their junior driver programme. It was announced that Russell would take part in both days of the Budapest test on the 1–2 August, which followed the Formula One World Championship and support series races at the same circuit from the weekend before. In November the same year it was announced that Russell would make his Formula One practice debut at the Brazilian Grand Prix driving in the first practice session for Force India. Subsequently it was announced that he would also drive for them in first practice session for the Abu Dhabi Grand Prix.

In January 2018 Russell was confirmed as a driver for ART Grand Prix for the 2018 FIA Formula 2 Championship, which would see the new Dallara F2 2018 make its debut in the expanding 12-race calendar. He was also confirmed as the Mercedes’ reserve driver, sharing duties with Pascal Wehrlein the following month.

Russell was announced as one of the Pirelli Tyre Test Drivers for Force India at the post-Spanish Grand Prix test in May 2018. He completed 123 laps for the team at the test, his first in a Formula One car with 2018 specifications.

On 13 October 2018, it was announced that Russell had signed a multi-year deal to drive for the Williams team, being partnered with Robert Kubica for the 2019 season. The team struggled during the season, with the Williams FW42 being the slowest car of the field. As a result, Russell’s competition during races was often only his teammate. He began to show signs of competition when he began to scrap away with the Toro Rosso of Alex Albon during the 2019 Austrian Grand Prix. At the rain-affected German Grand Prix, Russell crossed the line in 13th place before being promoted to 11th after the Alfa Romeo drivers were penalised post-race for using driver aids. He narrowly missed out on scoring his maiden point in Formula One, having been overtaken by Kubica in the closing laps.

Russell ended the season in 20th place in the championship being the only driver in the 2019 season not to score a point.

Russell continued driving for Williams in 2020, partnered by former competitor and 2019 Formula 2 runner-up Nicholas Latifi. He retired from the opening race in Austria from a loss of fuel pressure. For the Styrian Grand Prix Russell started the race in 11th after a wet qualifying, his highest Formula One grid start to date. An early trip to the gravel effectively ended Russell’s chances at points, and he finished 16th with both Williams drivers struggling for race pace.