The retrial to determine damages is underway in San Jose.
A previous jury had awarded Apple $1.05 billion after determining 26 Samsung products had infringed six Apple patents. But a judge found the jury miscalculated $400 million in damages for 13 products and ordered a new trial to determine how much Samsung should pay.
Samsung and Apple have been locked in bitter legal struggles around the world as they fight for supremacy of the more than $300 million smartphone market.
Despite the amount of money involved, the current proceedings are somewhat of a warm-up for a much larger trial scheduled for March. That trial will focus on newer products still on the market, while the current trial is a battle over products that are several years old and no longer sold in the U.S. Apple is asking that Samsung be barred from selling some of its current devices in the U.S., and more money will be at stake as well.
Apple Inc. has argued in courts, government tribunals and regulatory agencies around world that Samsung's Android-based phones copy vital iPhone features. Samsung Electronics Co. is fighting back with its own complaints that some key Apple patents are invalid and Apple has also copied Samsung's technology.
The two have each won and lost legal skirmishes over the last couple of years, and the companies appear oceans apart in settling their differences. Analysts predict continued litigation for months to come.
Apple transformed the mobile phone industry when it started selling the iPhone in 2007, but its success was quickly imitated and Samsung's smartphone shipments surpassed Apple's iPhone sales in 2011.
According to research group IDC, Samsung shipped 81 million devices in the July-to-September quarter for a market share of 31 percent, making it the world's top seller. Apple is a distant second, having shipped 34 million iPhones, for a market share of 13 percent over the same period.