Manufacturers want to have control of it all, but independent repair shops, fleet operators, insurance companies and anyone else who could benefit from this data, argue that this would be blatantly anti-competitive.
Policy wonks in the European Union are currently wrestling with the issue.
So why should you care?
Because it could mean that your car servicing costs become more expensive and you may have to pay more for other services that rely on such data, from independent repair centres to "pay-as-you-drive" insurance companies.
Modern cars are effectively computers on wheels, full of sensors measuring everything from the wear and tear on your brake pads to your fuel efficiency.
They are capable of communicating wirelessly with manufacturers, traffic management systems, and other vehicles in real time.
So your car's manufacturer probably knows where you've been, how fast you drove, and how soon you're likely to need a service.
And it wants to turn this knowledge in to money.
Say your car's onboard sensors detect that a certain part is about to fail. The manufacturer will have wireless access to that data and could then alert you and even book a service for you automatically.
That sounds convenient and useful, right?
But what if the repair centre is owned by the car manufacturer? You might not be getting the best price for the new parts and servicing. And what if their authorised repair centre is a lot further away than your local garage?
"While the manufacturer is monitoring the car, it has the power to recommend its own spare parts. This is a privileged position and would distort the market," says Neil Pattemore, technical director at FIGIEFA, the European association representing car parts retailers and repair shops.
"We exist to offer consumers choice - it's about freedom of where you want to get your car repaired."
The European Automobile Manufacturers Association (ACEA) is arguing that car makers should be allowed to send all this "in-vehicle" data to their own cloud platforms and control who has access to it and under what terms.
Allowing "direct third-party access to vehicular electronic systems would jeopardise safety, (cyber)security and vehicle integrity", it argues.
Manufacturers say they're worried about hackers taking control of a car's electronic systems, as has been shown to be possible on several occasions.
They also fear that allowing third parties to peer in to their cars' "brains" would jeopardise "trade secrets, know-how or information covered by intellectual property rights".
But a growing number of industry bodies think this has more to do with manufacturers trying to control a potentially lucrative business.
"In the connected era, every vehicle will have its own in-built telematics device and the functionality of a smartphone," says Gerry Keaney, chief executive of the British Vehicle Rental and Leasing Association (BVRLA).
"The data this generates opens up a whole new range of opportunities to develop driver-based infotainment or navigation services.
"It also promises to revolutionise the ways vehicles are maintained and managed, enabling vehicle owners to share them between multiple users, fix them before they break down or streamline the repair and servicing process.
"There are huge amounts of money to be made or saved here, but only if you have access to the vehicle data," he says.
At the moment all cars have to have an onboard diagnostic (OBD) port. This allows mechanics to plug in a cable and access the data stored in the car's computer or electronic control unit (ECU).
Under European law every manufacturer has to fit one, primarily so testers can gain access to emissions data and check that the vehicles comply with pollution regulations.
But, obviously, mechanics can only access the OBD when the vehicle is stationary. So unless they can access this diagnostics data wirelessly, they say they will be at a competitive disadvantage.
The ACEA says manufacturers would be prepared to share this kind of data with third parties through their own cloud servers or via "neutral" servers operated by other companies.
But Mr Keaney says his members and vehicle owners would then have to go "cap in hand" to the manufacturers to access it, and would probably have to pay for it.
"Independent service providers will suffer and there will be less choice for consumers and vehicle owners," he says.
The aftercare industry wants equal access to this wireless in-vehicle data and believes the technology is already here that could provide it securely.
Public cloud providers like Amazon Web Services and Microsoft Azure run programs called hypervisors that create virtual machines on computer servers. These virtual machines enable many different clients to store their data safely and separately on one computer, thereby saving computing resources.
It's the technology that has enabled cloud computing to take off in the way that it has.
"Cars could also run hypervisors that allow virtual environments and enable third parties to access car data in a safe and secure way," says FIGIEFA's Mr Pattemore.
Several other industry bodies - Cecra, FiA, ADPA, Leaseurope and others - agree, saying that an "in-vehicle interoperable, standardised, secure and open-access platform" would be preferable to preserve a competitive market.
This may be a complex issue, but it could directly affect the pound in your pocket. Expect to hear more about this in the months to come.
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An almighty row has broken out over who should have access to all the data new cars generate.