By Michal Lev-Ram
January 22, 2013

FORTUNE — If there is such a thing as a titillating patent trial, Apple v. Samsung makes the top of the list. In early 2011 the iPhone maker, based in Cupertino, Calif., filed a complaint against the Korean company, claiming that 28 Samsung devices infringed on Apple’s intellectual property — including a so-called design patent for a rectangular slab with rounded corners. Samsung countersued, alleging that Apple (AAPL) infringed on its patents for wireless communications technology.

At trial that summer each company got just 25 hours to make its case, and after three days of deliberation, a nine-person jury found that Samsung had willfully infringed on several of Apple’s design and software patents, and awarded the U.S. company $1.05 billion in damages.

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The verdict was a major blow to Samsung, which also lost its countersuit. But, of course, the story doesn’t end there. Apple then sought an injunction on several Samsung products, which was ultimately denied. (Apple is appealing.) In October, Samsung appealed the California jury’s decision, alleging that the jury foreman concealed information. And the two companies are still haggling over damages — a final decision from Judge Lucy Koh has yet to be issued. In the meantime, Apple and Samsung have been involved in litigation in other countries as well, with Samsung winning rulings in Japan and the U.K. A second U.S. case, with a new roster of allegedly infringing devices, is set to begin in 2014.

The outcome of these cases won’t be clear for several years, but so far neither company seems to be halting R&D or sales of the phones in question. So how will this duel be settled? Although it’s rare for the Supreme Court to rule on such cases, Apple v. Samsung may prove monumental — and titillating — enough to make it all the way to the highest U.S. court.

This story is from the February 4, 2013 issue of Fortune.

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