When Jaguar Racing entered Formula One in 2000 as a Ford subsidiary, the project struggled to find consistent direction. Niki Lauda and Bobby Rahal each came and went as team principals, and the results were rarely competitive. By the end of 2002, a wholesale change was underway. Tony Purnell and David Pitchforth assumed control of the team, Eddie Irvine retired from the sport after his contract expired, and Pedro de la Rosa was negotiated out of his agreement. The R4 was intended to be the first real product of this new era, with an emphasis on chassis stiffness and thorough pre-season development.
Designers focused on producing a substantially stiffer chassis compared to the R3 that had preceded it, aiming to address handling inconsistencies that had plagued earlier Jaguar machinery. A concerted programme of on-track testing and factory simulation work was planned to shake out reliability problems before the season began. Despite these intentions, the car arrived at the opening races having covered comparatively few kilometres as a complete package, delayed by reliability issues that compromised the pre-season schedule. Engine suppliers Cosworth performed well throughout the development phase, supporting both the hybrid chassis and the test programme.
Mark Webber quickly established himself as the faster and more committed of the two drivers. At the Brazilian Grand Prix he was involved in a heavy crash that triggered a red flag stoppage, though the incident also demonstrated the intensity he brought to every weekend. Over the course of the season Webber recorded a series of sixth- and seventh-place finishes, points that cumulatively pushed the team to sixth in the Constructors' Championship, their best result to that point.
Antônio Pizzonia's performances lagged well behind his teammate despite having access to the same machinery. After the Spanish Grand Prix reports emerged that Jaguar were pursuing McLaren test driver Alexander Wurz as a replacement, though McLaren ultimately retained Wurz to assist their own development work. This left Jaguar in an awkward position, backtracking publicly before eventually replacing Pizzonia with Justin Wilson following the British Grand Prix. Wilson, like Webber, was an alumnus of Minardi, making it the first time in team history that Jaguar fielded two former Minardi drivers simultaneously.
The R4 maintained the dark green livery that had characterised previous Jaguar entries, with subtle updates each race. At the Monaco Grand Prix the team took the unusual decision to repaint the leaping-cat nose emblem pink as part of a promotion for the Steinmetz Flawless Diamond Collection, tying the car's appearance to the unveiling of the 59.60-carat Steinmetz Pink diamond. At the British Grand Prix both cars ran special Terminator 3: Rise of the Machines branding on their airboxes.
The R4 season is generally regarded as the one moment when the Jaguar project appeared capable of growing into a genuine mid-field threat. Webber's results in particular attracted widespread attention and formed the foundation of a reputation that would carry him through to eventual championship contention at Red Bull Racing. However, Jaguar Racing would not build on the R4's relative success; Ford sold the team at the end of 2004 and it was reborn as Red Bull Racing, taking with it much of the technical infrastructure that had finally begun to show promise.