**Editor's Note: Click here for our most recent list of hottest selling smartphones to see how the iPhone and Samsung handsets fared against the competition, or here for our top 10 list of best smartphones in 2013 (so far).**
Apple's attorneys are arguing for $379 million, while Samsung says the number should be closer to $53 million.
This week's legal proceedings are the start of a retrial. A jury awarded Apple more than $1 billion last year when it agreed that Samsung copied a number of features from the iPhone on its own devices, Reuters said.
In March, a U.S. District judge said that the jury made some miscalculations in their decision that impacted about 40 percent of the final verdict. It's that portion that's being retried.
Apple claims that Samsung sold about 10.7 million devices that infringe on Apple's patents, totaling about $3.5 billion in revenue.