DAMS entered the International Formula 3000 Championship a year after its 1988 foundation. It became immediately competitive, winning the drivers' championship in 1990 with Érik Comas, in 1992 with Olivier Panis, and in 1994 with Jean-Christophe Boullion. Over thirteen seasons in Formula 3000, from 1989 to 2001, DAMS accumulated four team titles, three drivers' championships, 21 wins, 19 pole positions, and 19 fastest laps — establishing itself alongside Super Nova Racing and Arden International as one of the most decorated teams in the series. DAMS was also part of the Elf young driver sponsorship programme.
The team briefly planned an F1 entry for 1996, with a car designated the GD-01 designed by Reynard, but insufficient funding prevented the project from advancing.
DAMS entered the GP2 Series from its launch in 2005. An association with the Toyota Drivers Program between 2006 and 2009 brought drivers including Kazuki Nakajima and Kamui Kobayashi to the team. The Renault Formula One connection proved more fruitful: Romain Grosjean dominated the 2011 GP2 Asian and main series championships driving for DAMS under a Renault partnership. Davide Valsecchi won the 2012 championship, while Felipe Nasr's consistent scoring helped DAMS clinch its first GP2 Teams' Championship that year.
Jolyon Palmer won the 2014 drivers' title with DAMS. Nicholas Latifi led the team to the 2019 FIA Formula 2 Teams' Championship with five wins, while Alexander Albon delivered four wins in 2018. The 2018 lineup of Latifi and Albon would later race together again in Formula One with Williams in 2022.
DAMS entered Formula E in 2014 as e.dams, partnering with Alain Prost. Sébastien Buemi claimed the 2015-16 drivers' championship with the team after finishing runner-up in the inaugural season. e.dams won three consecutive constructors' titles. The partnership transitioned to Nissan from the 2018-19 season, though championship success proved elusive under that banner. Nissan eventually parted ways with DAMS after successive poor results in 2021 and 2022.
Starting from 1997, DAMS diversified into sports car racing, entering the FIA GT Championship and later competing at the 24 Hours of Le Mans. In 2000 and 2001, DAMS managed the works Cadillac Northstar LMP prototypes in the American Le Mans Series and FIA Sportscar Championship in partnership with General Motors. The team also supported the Michel Vaillant movie production in 2002 by preparing and racing cars at Le Mans.
DAMS has served as a launchpad for some of motorsport's most prominent names. Formula One race winners who drove for DAMS include Olivier Panis and Pierre Gasly. Among 24 Hours of Le Mans winners who passed through the team are Allan McNish, Sébastien Bourdais, Kazuki Nakajima, Sébastien Buemi, Neel Jani, Kamui Kobayashi, and José María López. Bourdais went on to win four consecutive Champ Car World Series titles; Marcus Ericsson won the 2022 Indianapolis 500. Championship-winning DAMS alumni also include Kevin Magnussen and Carlos Sainz Jr. in the World Series by Renault.
Jean-Paul Driot, the team's co-founder, died in August 2019 aged 68. His sons Olivier and Gregory Driot assumed co-team principal roles. In February 2022, former Formula 1 driver Charles Pic completed the purchase of the team. DAMS continues to compete in FIA Formula 2 and FIA Formula 3.