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 At this point, I have been through some of the "bounties" in Diablo 3. Bounties are a gameplay feature of Diablo III. They are a randomized objective system. They are marked on the waypoint map by yellow exclamation marks. There are 25 Bounties 

Rewards are not displayed when choosing a Bounty on the map. Typical rewards include gold and experience. Horadric Caches are rewarded for completing all five Bounties of an act.

There are five types of Bounties: Kill a Boss, Kill a Super Unique, complete an Event, Clear a Dungeon, and Exploration. Only one Bounty per zone is allowed in a single game. When close enough to the objective, the target is highlighted on the map (exact distance depends on the zone size). Most Bounties, except Bosses, can be accessed from two sides (by teleporting to the next zone and going backwards), which is helpful for completing a Bounty as soon as possible. A flashing icon also appears on the map, guiding the player to the main target of a bounty. Depending on bounty type, it can either appear immediately as the zone is entered, or after 1 minute.

Kill a Boss

This is a standard fight with one of the bosses (not necessarily main bosses) of each Act. However, all teleports located right before the bosses are disabled, so that the player always needs to get through at least one zone. The only exception is Zoltun Kulle, as there is no combat zone before the Soulstone Chamber. When a bounty boss is killed, a Radiant Chest (named Diabolic Hoard) appears, in addition to normal loot.

Kill a Unique

One Unique or Super-Unique monster in the zone is nominated a target (does not prevent other Uniques and Super-Uniques from spawning in the same zone). In addition to that monster, player must also kill a number of other enemies in the same zone, the amount varying depending on the zone size (25 to 150). The only exceptions are monsters that spawn in very small zones, such as Hell Rift.

Event

The player must successfully complete a specific event. These include scripted events, cursed chests and shrines, and even unmarked events. Bonus objectives have no effect on Bounty reward.

Clear a Dungeon

The player must kill all enemies (except resurrected and summoned foes) in the dungeon, the most bottom level only in case of multi-tiered dungeon. When 15 or less enemies remain, they are highlighted on the map. Only small dungeons with no more than 100 enemies can roll for this type of Bounties.

Exploration

Exploration involves events that require exploring an area and finding people who need to be rescued (if they're friendlies) or slain (if they're not).

I have done about 12 bounties at this point. The rewards are significant and it adds a fun element to the gameplay.