The car was unveiled at a pre-season test session in Valencia on 23 January 2008, a week before its official launch. The official reveal took place at the team's operational base in Brackley, England. Rubens Barrichello drove the car at the Valencia test.
For 2008, Honda made significant changes to its management structure. Ross Brawn was appointed team principal, a major coup given his record of championship success. Jörg Zander, formerly chief designer at BMW Sauber, joined as deputy technical director. The driver lineup of Jenson Button and Rubens Barrichello was retained from the previous two seasons.
The 2008 regulatory environment posed new challenges for all teams. The FIA mandated the use of a single gearbox across four consecutive races and introduced a standardised McLaren Electronic Systems ECU that eliminated driver aids including traction control and engine braking. Brawn acknowledged publicly before the season began that the team's primary focus was on the 2009 car — a point that would prove prescient.
Pre-season testing did not provide encouragement. Button described the RA108 as lacking "driveability" as the team adapted to the new technical regulations. Brawn stated openly that the team had a better chance of success in 2009, when an entirely new regulatory framework would level the competitive playing field.
Development of the RA108 continued through the season. A revised aerodynamic package was introduced at the Spanish Grand Prix, featuring a modified nose design nicknamed "dumbo" wings. A second iteration of this nose appeared in testing at Paul Ricard ahead of the Monaco Grand Prix. At the Turkish Grand Prix, Barrichello's car carried a special commemorative livery marking his 257th race start, which broke the previous record held by Riccardo Patrese.
The car's livery again featured the Earth imagery introduced on the RA107, with modifications including horizontal stripes at the front and red accents continuing the Earth Dreams environmental campaign, alongside the Type R Honda emblem on the nosecone.
The RA108 was a consistent mid-to-rear-field car throughout the season, unable to repeat even the occasional strong results of the RA107's campaign in China the previous year.
In December 2008, Honda announced it was withdrawing from Formula One with immediate effect, citing the global financial crisis. The decision came after the 2008 season had concluded and the 2009 car — internally designated the RA109 — was already substantially developed. Ross Brawn purchased the team from Honda for a nominal sum, renamed it Brawn GP, secured a supply deal for Mercedes engines, and entered the 2009 season with the car Honda had designed as its successor. Jenson Button won the Drivers' Championship and Brawn GP won the Constructors' Championship — titles Honda had funded the development of but did not live to collect.
The RA108 was subsequently repurposed in several ways. It was fitted with a 2009-specification front wing and a KERS system for continued testing use. Later it was displayed as a show car running the livery of the Brawn BGP001, and subsequently with the liveries of the Mercedes W01 and W02. In 2014 the car was again used as a demonstration vehicle for pit stop challenges, fitted with the rear wing and monoblock wheels from the Mercedes W05 — a chain of reuse that traced the institutional lineage from Honda through Brawn to Mercedes in a single physical object.
Honda did not return as a Formula One engine supplier until 2015, when they partnered with McLaren to power the MP4-30.