Almost nobody does this today. Software and data all still reside on physical servers, but they sit in cavernous buildings hundreds of miles away, protected by near-military grade security.
Instead of buying the servers outright, companies pay the operators of those data centres - the three biggest of which are Amazon, Google and Microsoft - for access to them.
This so-called public cloud barely existed a decade ago, but was a $257 billion industry last year. Amazon is the sector's biggest player, with its cloud computing arm, AWS, generating more profit than the company's entire retail division.
The cloud is a marvel. It has enabled multibillion-dollar companies that would otherwise have failed to grow rapidly enough to gain traction. Anyone, with almost no capital, can spin up a web service and offer it to the world.
Or, at least, almost anyone. Last week, Amazon shut off cloud services to Parler, a social network that had become popular among Donald Trump's most aggressive supporters, following claims that the Washington DC rioters of January 6 had used it to plan their assault on the US Capitol building.
AWS told Parler that calls for violence it had found on the service violated its terms of service. On Monday morning, Parler went dark, and despite the company's efforts, it remains offline, quite possibly for good.
AWS's concerns about Parler appear genuine. Before, during and after the riots, the site held plenty of violent content. The company also has no obligation to continue to take Parler's business. Just as US laws give social media sites immunity for what is posted on them, Amazon can deny service to those it judges to have violated its terms.
Parler has taken Amazon to court, claiming the move was breaking competition laws, but the argument - that it was conspiring with Twitter to suppress a rival - was presented without evidence.
But while the company seems to be within its rights - and even if taking Parler offline was the right decision - we can still worry about the effects of Amazon's move. In the last week, a substantial amount of anger at Big Tech has been directed at Twitter and Facebook, which removed Trump from their services after the riots.
Republicans have accused the platforms of censorship; Democrats say if they had acted sooner, there would have been less fuel for those who stormed the Capitol.
But even many of those who believe the social networks made the right call have bristled at Amazon's move. The American Civil Liberties Union drew a line between Twitter, which it called a "speech community", and Amazon, which "really holds the keys to the internet".
Twitter's own chief executive Jack Dorsey was worried that "a number of foundational internet tool providers decided not to host what they found dangerous", setting a troubling precedent.
The distinction is that the two services exist at fundamentally different layers of the internet. While Twitter is at the surface, a consumer product that few parts of the economy actively rely on, AWS is more like infrastructure; the plumbing of the web.
The water or electricity company does not cut off a customer because they disagree with them, and while AWS is not exactly a utility, it is perhaps closer to one than the social networks are. Its power to shut off sites because it deems their moderation to be inadequate raises questions, at the very least.
The same is true of other infrastructure providers, such as Twilio and Okta, which also ditched Parler last week. Moderating speech is certainly Twitter's job, is it Amazon's?
These concerns are not new. AWS shut down WikiLeaks after the site published classified US documents. Many online retailers refuse to use Amazon's service, perhaps concerned at placing their data and operations in the hands of a company that competes with them.
But while most retailers find it easy to find an alternative cloud provider, Parler has had no such luck, saying last week that AWS's refusal to host it places the company on life support.
The events surrounding the end of Trump's presidency are so unique that it might be an overreaction to worry about precedents being set. But plenty who agree with tech companies' decisions to take Parler offline will still find themselves concerned about where power sits.
If regulation is to follow, the idea of cloud neutrality - that the services such as AWS that underpin the web should provide equal access to anything within legal limits - may well come into fashion.
The social media giants have taken much of the flak for cracking down on Trump and his supporters. The lesser-known companies that provide the internet's infrastructure could well face longer-term consequences.