(FORTUNE Magazine) – Since the invention of the PC, techies have taken two things for granted: Processor speeds will grow exponentially, and PCs will become indistinguishable from televisions--that there will be, in industry lingo, convergence. The first prediction obviously has come true (nice crystal-ball gazing, Gordon Moore!), and the second--well, consumers aren't exactly firing off e-mail from their TV sets.

So what are Michael Dell and Carly Fiorina doing hawking flat-screen TVs? And why, while we're at it, is Fiorina waving around an iPod at the Consumer Electronics Show? It turns out that after a generation of hype, convergence has actually become real--and, over the next few years, it's going to be huge, if a little different from what we once imagined. Consumers may not like to watch movies on their PCs, but they love listening to music on them. They may not like to send e-mail from their couch, but they love having a PC--known as a digital video recorder--attached to the TV to automatically record all their favorite shows. And while they won't buy an old-fashioned TV from Dell or HP, when it comes to flat-screen TVs, they have no problem at all.

Why is convergence happening now, after all these years? Thank the cheap flat screens and hard drives, easy broadband access, and simplified home-network setup. Today, hard-drive storage--the guts of an iPod or DVR--costs less than $1 a gigabyte, down from $20 a gigabyte in 1999. Flat-screen TVs that cost $10,000 a few years ago now goes for less than $1,000.

For PC makers, it's also good business. Prices and margins for computers keep falling; gross margins in consumer electronics are twice those in the PC world. And now that the music and movies consumers play on those systems are the same zeros and ones that are the foundation of PCs, there is little conversion cost.

The only clear winner in this new world is Apple, which has leveraged its computer platform to make it easy and fashionable for consumers to get with the digital-music age. Apple today sells almost as many iPods per quarter as it does Macs. Microsoft wants in on this business badly, but as HP's decision to shift its loyalty to Apple illustrates, Microsoft doesn't have much leverage just now. The other company to watch over the next few years is Sony. It misplayed the convergence game but is redoubling efforts to make its PC, consumer electronics, gaming, and entertainment divisions play together. Whoever wins the hearts and minds of consumers, one thing's clear: The eye-rolling over convergence can stop right now. --F.V.