The following events will occur during races.

Avoid: Triggers when multiple cars in front of you crash into a big pile up. Avoid them by dragging a line directing your car around the pile up.
Block: Triggered when the racer behind you is riding on your slipstream. They will approach you from behind, then suddenly approach from the right or left. To counter them, quickly swipe in the direction they are approaching.
Overtake: The view will change to first person perspective. Tilt your device to turn correctly. Do not tilt too far or you may collide with the car you are trying to overtake.
Pit Stops: Triggered when you run out of fuel and tires or if manually activated. Your car will pull into the pit stop for a tune up, and five blue circles will appear on your tire. Quickly tap all the circles to remove your tire. A new tire will replace it, and you must tap the circles again to return to the race.
Slipstream: Triggered when you draft the racer in front of you. Wait until you are close to the leading car, then swipe left or right to race around them. Wait as long as possible without crashing.