Random events returning
Random events are a much loved feature of Diablo 3 and Path of Exile. They'll make a return in Diablo 4 [1], randomly spawning in the game's over one hundred Dungeons:
"Random events are back. Random events are a core part of the classic dungeon crawling feeling in Diablo 4. One major change to the past game is they're no longer restricted to a specific place in the world. This allows dungeons to have a much broader range of possible events. Every time you play, you can find a different type of event in it."
Diablo 4 SteelSeries hardware
Altar of Bishibosh random event
Blizzard gave us a glimpse of one random event called Altar of Bishibosh, in which the player's goal is to destroy an altar while also defending against a horde of monsters. "Event joined" is shown on the screen, which may indicate that a player must opt-in to random events.

Experience & gold as rewards
After successfully completing a random event, a message pops up on the screen showing the player's reward: experience and gold. We don't know if rewards are limited to these two things, but most likely.

Trending hardware for Diablo 4
Sources
Article | Source | Date | |
---|---|---|---|
1. | 2019 BlizzCon: Diablo IV Systems and Features | Blizzard |
Changelog
Ver | Change | Date | |
---|---|---|---|
Alpha | Added section on random event rewards | ||
Alpha | Published original |