The trial began on Monday - and is one of the most important in Apple's history.
Apple boss Tim Cook will be giving evidence, the first time he's given testimony at a trial.
At stake is the future of the App Store and the amount it charges developers - a wildly lucrative money spinner for the company.
The trial got off to a slightly chaotic start. The public hearing failed at first to mute those who were listening in via phone call, meaning calls from fans for the return of Fortnite to mobiles were accidentally broadcast.
The storm began in August last year, when Epic Games laid a trap for Apple.
Its hit game Fortnite implemented its own in-app payment - bypassing Apple's 30% charges.
Apple promptly kicked Epic Games off the App Store.
But Epic Games was waiting for just that.
It slapped Apple with a 65-page lawsuit - and had even prepared a high production video, a spoof of Apple's iconic 1984 advert for the Apple Mac
Epic Games has for years claimed the charges imposed on it by Apple are extortionate.
Their argument is simple: that Apple's control over the App Store is anti-competitive.
It believes that developers should be able to make apps for smartphones without having to pay large sums to Apple (and to Google for Google Play purchases).
Spotify, Match and Tile are just a few of the many companies that have also claimed Apple's charges are unfair.
Apple is estimated to have made hundreds of millions of dollars from Fortnite alone in charges.
Epic Games' big argument is: if they don't want to pay, then where else do they go to sell their products?