Inverter cards are used to change key events (i.e. flip over Linchpin cards, which causes the Ripple Point cards to become paradoxes). There are several different kinds of Inverters. Some allow you to flip any Linchpin you want, some allow you to restore history by flipping a red linchpin back to black. There are even some custom purpose ones, such as an inverter that can only be used to prevent an assassination.
The patch cards are of course used to patch paradoxes on the timeline, which also allows you to draw an extra card into your hand.
