The case began in 2011 after Apple’s late founder Steve Jobs declared “thermonuclear war” against the Android (GOOG) operating system that powers Samsung smartphones, and will likely end next year.

Here’s a plain English guide to the case based on interviews with patent experts, lawyers, and sources close to Apple and Samsung:

Why are Apple and Samsung at the Supreme Court?

The companies’ trip to the top court is the latest twist in a saga about whether Samsung devices like the Galaxy S phone copied early versions of the iPhone. At this point, it’s pretty much settled that Samsung infringed on Apple’s intellectual property—but now the Supreme Court has to step in to explain a law about how much it should pay.

The legal fight has involved all sorts of intellectual property issues, but the top court is examining just one of them: How much a design patent should be worth.

When is the hearing?

Apple (AAPL) and Samsung (SSNLF) will square off at 10 a.m. ET on Tuesday at the Supreme Court. The hearing will last about 90 minutes with each side making arguments, and the U.S. Justice Department offering its two cents as well.

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What’s a design patent?

Most people don’t realize there are two types of patents: utility patents and design patents. Utility patents, which are far more common, protect new machines and other inventions. Design patents instead cover the ornamental parts of an invention that make is distinct.

The point of design patents are to ensure that a product’s artistic elements, which are ineligible for copyright, can still be protected. Design patents can cover things like cars or spoons—or the look of Apple’s iPhone.

What’s so special about the iPhone design?

A jury found that Samsung infringed not just one, but three of Apple’s design patents. One covers the early iPhone’s black rectangle shape with rounded corners, and another covers the raised frame (aka the bezel) that holds the screen to the rest of the phone. The last one covers the layout of 16 colorful icons on the screen.

Here’s a picture from the bezel patent. (Note that under design patent rules, the solid lines are covered by the patent while the dotted lines represent parts of the design that are not covered)

So what’s the legal issue?

It’s not about whether Samsung infringed the patents. Instead, the fight is over how much the company should have to compensate Apple under a law that says it must pay the “total profit.”

An appeals court ruled Samsung should hand over all of the profits it earned from products that infringed on the iPhone’s design. Samsung says this is unreasonable and it should only be on the hook for the value represented by the copied features.

The case could turn on another phrase in the statute that refers to an “article of manufacture.” In this case, this would mean determining if the “article of manufacture” is the entire iPhone or instead just the patented features—such as the icon layout or the black rectangle look.

What are each side’s best arguments?

Apple is basically saying, “Look, the law is very clear: ‘Total profit’ means ‘total profit,’ and Samsung should pay up.” While it concedes that “article of manufacturer” can mean individual design features (rather than the whole product), Apple claims Samsung failed to make that argument in this case so the matter is settled. It wants the Supreme Court to reject Samsung’s appeal.

Samsung is making more of a policy based argument, saying “Come on, it would be crazy for one little design feature to account for the entire profit of a product. That’s like saying a design patent for a car door handle should be valued on the basis of an overall car.” Samsung wants the Supreme Court to throw out the verdict altogether or return it for a new hearing based on the value of the design patents.

Apple, though, has a policy argument of its own. It points out that Congress changed the design patent law in 1887 to add the “total profit” wording, and the reason it did so was to make sure copycats didn’t get off lightly.

So who’s going to win?

This one’s hard to predict, not least because the Supreme Court last ruled on design patents more than 100 years ago. The court’s conservatives, Justices Thomas and Alito, will be receptive to Apple’s “the law says what it says” argument. But on the other hand, Samsung has a good point that it’s absurd to claim anyone values any smartphone (bet it a Galaxy or an iPhone) entirely on a design feature—rather than for what it does.

Sarah Burstein, an authority on design patents at Oklahoma University, suggests the Supreme Court will at least chip away at what some are calling a draconian rule set by the appeals court:

“In this case, the Federal Circuit has created a rigid, bright-line rule. In a lot of recent IP cases, the Court has rejected rigid bright-line rules created by the Federal Circuit in favor of standards or multi-factor balancing tests. So it wouldn’t be surprising to see the Court do that here.”

There’s also a good chance the Supreme Court will heed the Justice Department, which it invited to weigh in on the case. According to the feds, the court should preserve the “total profit” rule but also interpret “article of manufacturer” on a case-by-case basis — meaning sometimes the design patent will cover a whole product, and sometimes just a part of it. In this case, the Justice Department recommends a new trial.

Who’s taking Apple’s side? And Samsung’s?

Both Apple and Samsung have some powerful friends who submitted briefs on their behalf. On Samsung’s side, the allies include an influential group of law professors, trade associations like the Internet Association and the CCIA that represent the likes of Facebook (FB) and Amazon (AMZN), and open software advocates.

Apple, meanwhile, has support from an association of industrial designers, patent lawyers, and well-known companies like Adidas and Tiffany & Co (TIF).

What happens next?

The Supreme Court’s ruling will probably come out in December or January. If Samsung wins outright, the court will order Apple to repay the $399 million in design patent damages it collected last year from Samsung. Or it will let Apple keep it all.

A more likely outcome is the court sends the case back to a lower court, where the damages will be chopped down. Meanwhile, the outcome will determine another Samsung-Apple case now on hold over different design patents.

I can’t get enough of this stuff. Where can I read more?

Fortune will be at the Supreme Court hearing on Tuesday. There are no phones or computers (and no Twitter!) allowed in court, so we’ll have a report published online shortly after it concludes.

You can also read more about the case here on SCOTUS blog, which has a summary plus all the briefs. And if you want to delve into the long, messy history of Apple and Samsung suing each other all over the country, the Verge has a full timeline. Have fun!