Nelson Piquet launched the team in 2000 with Filipe Vargas managing operations. The squad's first competition was the South American Formula Three Championship, where Piquet Jr. finished fifth in the drivers' standings. The following year, the team was dominant: Piquet Jr. won thirteen of eighteen races to claim the drivers' title, with Piquet Sports securing the teams' championship by more than a hundred points over their nearest rivals.
The team crossed to Europe in 2003, entering the British Formula Three Championship. Piquet Jr. took six wins over the course of the season with five additional podiums, finishing third in the final standings behind Alan van der Merwe and Jamie Green. In 2004, the team split its activities between British Formula Three and the South American championship, entering fellow Brazilian Alexandre Negrão in the latter. Both drivers took their respective championships, with sixteen wins between them that year.
Piquet Sports graduated into the GP2 Series in 2005 — the newly created championship that replaced Formula 3000 as the primary feeder series to Formula One — entering Piquet Jr. and Negrão for their debut campaign. A brief association with British operation HiTech Racing was formed but terminated mid-season. Piquet Jr. took a single win at Spa-Francorchamps as the team finished sixth overall.
The 2006 season was Piquet Sports' most competitive to date. Piquet Jr. won four races and pushed Lewis Hamilton all the way to the final rounds of the title fight, ultimately finishing as runner-up to the Briton by twelve points. Piquet Sports similarly fell short of ART Grand Prix in the Teams' Championship. The season nonetheless established the team as a legitimate title contender.
Piquet Jr. departed at the end of 2006 to join Renault as their Formula One test driver, leaving a substantial gap in the team's leadership.
Ahead of the 2007 season, Piquet Sports merged with GP Racing — a team founded by Tancredi Pagiaro in 1997 that had been active in Italian Formula 3000 and the Euroseries 3000, winning the drivers' and teams' titles in the latter competition in 2007 with Davide Rigon and Diego Nunes — under the combined banner Minardi by Piquet Sports, licensing the Minardi name from Giancarlo Minardi via the GP Racing partnership. Spaniard Roldán Rodríguez replaced Piquet Jr., while Negrão remained with the team. The newly merged outfit achieved limited success in the 2007 GP2 season, collecting 22 points and finishing outside the top ten in the standings.
For 2008, the Minardi name was dropped and the team competed simply as Piquet Sports. Venezuelan Pastor Maldonado, who had won in Monaco the previous year, joined the squad and took the team's first pole position in the series at the opening round in Catalunya. Italian Marco Bonanomi claimed a win in the GP2 Asia Series that season. The year also marked the team's final campaign in the Euroseries 3000.
During the 2002 South American Formula Three season, rival teams lodged protests against Piquet Sports alleging illegal testing. The team argued that newly installed mudflaps classified the car as a prototype model, and no punishment was imposed.
For 2009, with all remaining ties to the Piquet family severed, the operation was renamed Piquet GP and then Rapax Team by November of that year. The GP Racing half of the partnership carried forward the technical foundations, while the Piquet name disappeared entirely from motor racing.