The long-running dispute between the two tech giants relates to patent infringements and has already cost Samsung around $930 million (£558 million).
Apple is now launching another bid and is seeking a whopping $2 billion (£1.2 billion).
Features in question include tap-from-search feature that allows you to call a phone number found online and the "slide to unlock" feature.
Court filings said: "Apple revolutionised the market in personal computing devices.
"Samsung, in contrast, has systematically copied Apple's innovative technology and products, features and designs, and has deluged markets with infringing devices."
Samsung has launched a counter-claim insisting Apple has infringed on patents relating to wireless technology in devices.
They said: "Samsung has been a pioneer in the mobile device business sector since the inception of the mobile device industry.
"Apple has copied many of Samsung's innovations in its Apple iPhone, iPod, and iPad products."