DAMS entered the International Formula 3000 Championship the year after its foundation in 1988 and remained in F3000 until 2001. As part of the Elf young driver sponsorship programme, the team became one of the most successful operations in the series. DAMS won the F3000 Drivers' Championship three times — with Érik Comas in 1990, Olivier Panis in 1992, and Jean-Christophe Boullion in 1994 — and claimed four Teams' Championships across thirteen years. In total the team scored 21 wins, 19 pole positions, and 19 fastest laps in F3000.
The team planned an entry into Formula One in 1996 with a car designated the GD-01, developed by Reynard, but lack of funding prevented the project from reaching the grid.
When Formula 3000 became the GP2 Series in 2005, DAMS continued to compete and soon established itself among the top teams in the new formula. A close association with the Renault Formula One team shaped the squad's identity for several seasons. Romain Grosjean proved the team's most successful driver in this era, claiming both the 2011 GP2 Asia Series and the 2011 GP2 main series titles in dominant fashion. Davide Valsecchi followed by winning the 2012 GP2 Drivers' Championship with the team, while DAMS simultaneously took the 2012 Teams' Championship — its first in the GP2 era. Jolyon Palmer completed a strong run of titles by winning the 2014 Drivers' Championship.
The team's association with the Toyota Drivers Programme from 2006 to 2009 brought notable drivers through the ranks, including Kazuki Nakajima, who progressed to a full Formula One season with Williams, and Kamui Kobayashi, who became a Toyota Racing test driver and later a race winner in Formula One.
In the FIA Formula 2 era, DAMS fielded Alexander Albon and Nicholas Latifi in 2018, a pairing that eventually reunited as Williams Formula One teammates in 2022. The team won the 2019 Teams' Championship with Latifi and Sérgio Sette Câmara, Latifi going on to Formula One with Williams the following year.
DAMS entered Formula E in the inaugural 2014-15 season under the e.dams banner, in collaboration with Alain Prost. The partnership with Renault proved highly fruitful: Sébastien Buemi finished runner-up in the first season and won the championship in 2015-16 with eight wins and thirteen podiums in twenty-three races. Nicolas Prost provided additional points support, claiming three victories. DAMS also claimed the Teams' Championship in both 2015-16 and 2016-17, though Buemi narrowly lost the 2016-17 Drivers' title to Lucas di Grassi at the final round in Montreal.
The team transitioned to a Nissan powertrain for the 2018-19 season, fielding Buemi alongside Oliver Rowland. After Nissan departed at the end of the 2021-22 season following two poor campaign results, the manufacturer took over running the team directly.
From 1997 to 2002, DAMS diversified into sports car racing. The team entered the FIA GT Championship in partnership with Panoz, then ran prototype machinery in the SportsRacing World Cup, winning four races. DAMS also competed in the American Le Mans Series, prepared Cadillac Northstar LMP prototypes in association with General Motors in 2000 and 2001, and participated in the 24 Hours of Le Mans on multiple occasions.
In the A1 Grand Prix series, DAMS operated A1 Team France — which Jean-Paul Driot co-owned — and managed A1 Team Switzerland, A1 Team Mexico, and A1 Team South Africa. A1 Team France became the first winner in the series history, claiming thirteen of the twenty-two races in the 2005-06 season.
DAMS has launched or supported the careers of numerous prominent figures in motorsport. Formula One Grand Prix winners who drove for the team include Olivier Panis and Pierre Gasly. Sébastien Bourdais, who raced for the team in supporting roles, went on to win four consecutive Champ Car World Series titles, while Marcus Ericsson won the 2022 Indianapolis 500 after developing with the team. Kevin Magnussen and Carlos Sainz Jr. both won titles in the World Series by Renault while associated with DAMS.
Founder Jean-Paul Driot died in August 2019 at the age of 68. His sons Olivier and Gregory Driot took over as co-team principals until former Formula One driver Charles Pic purchased the team in February 2022, taking the operation into a new chapter of its history.