The squad began life in the Spanish domestic road racing championship (Campeonato de España de Velocidad) under the By Queroseno Racing name. Between 2005 and 2008 it won three Fórmula Extreme titles with José David de Gea and two 125GP class titles with Stefan Bradl and Efrén Vázquez. After years of wildcard World Championship appearances, BQR became a full-time Grand Prix entry in the 2001 season, using Honda machinery in the 250 cc class. The team switched to Aprilia equipment in 2007, and in 2008 Scott Redding delivered BQR its first outright World Championship race victory at the British Grand Prix in the 125 cc class.
Following the introduction of the Moto2 class, BQR unveiled a prototype machine in February 2009 and competed in the Spanish championship before entering the inaugural Moto2 World Championship in 2010 with Yonny Hernández and Mashel Al Naimi. The team remained in Moto2 through 2013, then made further wildcard Moto2 appearances in 2018 with Xavi Cardelús.
In 2012 the team changed its name to Avintia Racing following an alliance with the Grupo Avintia. That same year it debuted in the MotoGP premier class as a Claiming Rule Team, fielding FTR Moto and Inmotec chassis powered by Kawasaki engines for Iván Silva and Yonny Hernández. In 2013 Avintia continued with Kawasaki-engined FTR frames for Hiroshi Aoyama and Héctor Barberá.
For 2014 Mike Di Meglio replaced Aoyama, and the team fielded the Avintia GP14, a machine reportedly derived from the 2007–2009 Kawasaki Ninja ZX-RR. Mid-season, a new agreement with Ducati brought Barberá an Open-specification Desmosedici for the final five rounds, beginning a long relationship with the Italian marque. From 2015 the team ran full-season Ducati Desmosedici Open-class bikes, and Barberá remained a regular fixture in the squad across several seasons.
In 2017 the team traded under the Reale Esponsorama Racing banner. In 2018 Tito Rabat and Xavier Siméon were the riders; Rabat suffered a severe crash at the British Grand Prix involving Franco Morbidelli that broke his right leg in three places, sidelining him for the rest of the season. Christophe Ponsson and Jordi Torres filled in as replacements.
For 2020 the team officially became Esponsorama Racing in line with its registered company name, though Grupo Avintia remained a main sponsor. The season paired Rabat with Johann Zarco, who arrived as a KTM factory exile and brought direct Ducati factory support with a one-year-old Desmosedici specification. The 2021 season was arguably the team's highest-profile year: 2020 Moto2 World Champion Enea Bastianini and Luca Marini joined, both on 2019-specification Desmosedici machines. Marini competed under a separate Sky Racing Team VR46 livery by agreement with the VR46 organisation. Bastianini proved especially strong, and his results attracted significant attention in the paddock.
At the end of 2021 Esponsorama announced its withdrawal from the MotoGP class after ten seasons; the VR46 team took over the grid slots. The outfit then refocused on Moto3 and MotoE activities before leaving Grand Prix racing entirely after 2022.
Avintia debuted in Moto3 in 2017 with wildcard entries for Vicente Pérez, then took a full-season slot from 2018 onwards. The class was used to develop lower-profile Spanish and international riders including Livio Loi, Stefano Nepa, and Carlos Tatay. In MotoE, as a Ducati satellite partner Avintia was awarded an entry in the inaugural 2019 MotoE World Cup, where Eric Granado delivered two victories and the team finished third in the championship.
Team BQR/Avintia/Esponsorama spent more than two decades as a reliable, low-budget presence in the Grand Prix paddock, giving opportunities to riders and engine manufacturers — including Kawasaki's transitional exit from MotoGP — that might otherwise have found no representation. Its willingness to pioneer the Claiming Rule Team concept from 2012, and later to run Ducati machinery that bridged factory and satellite relationships, helped define the structure of the modern MotoGP satellite grid. Enea Bastianini's strong 2021 performances under the Esponsorama banner earned him a factory Ducati seat the following year.