Events are unlocked after completing the Expert achievement. Upon unlocking, a random event has a small chance to occur after a fight, which you can choose to either accept or decline. There are six different types of events, as seen below.
An offer to receive a number of items, but you will have to fight a set of monsters afterward on the floor you got the challenge.
Reroll the class of one of your heroes to another one with the same tier
and color (Always a non-generated hero)
Swap the position of a hero in your team with another hero in your team (No side-effects)
Smash your second highest tier item into tier 3 item(s). The number of T3 items is equal to the smashed item's tier divided by 3 and rounded up.
If you smash a tier 0 item or below, it will remove the item without
giving back anything
Combine all your tier 0-3 items into a higher tier item:
At the end, result is rounded down to closest integer. If there is no item in that tier, you will get Bug. If you don't have any item to combine, you will get a free tier 0 item upon accepting.