What anime comes after Danganronpa the Animation?????!!?!?

The DanganRonpa chronological timeline is:

1. DanganRonpa 3: Despair Arc[anime that aired this year] It tells the very beginning of the DR story

2. DanganRonpa Zero [it's a novel] It covers some events Despair Arc didn't go over, and it's set before DR Animation.

3. DanganRonpa the animation/DR game - The anime is okay, but it skips and rushes lot due to lack of time. If you want to see the "let's play" videos or play the actual game you will get to know more detailed info.

4. DanganRonpa Another Episode - Despair Girls [a game] This game shows us what is happening outside and a few DR Animation/DR1 characters appear but they are not the main characters.

5. DR2 [it's a game] This game was the game that was released after the first game. Even though it's chronologically after Despair Girls I would recommend you see the 'let's play' videos before it. The main ending of this game is very important to understand what triggered DR3 Future arc.

6. Killer Killer [manga] - New characters that don't appear in the anime as main cast. Few appearances from past cast.

7. DanganRonpa 3: Future Arc [anime that also aired this year] Consequences from DR2 and a few new faces.

8. Hope Arc [this is just one 23 min episode] This is the end of the end of this DR universe, it was the highly critiqued by fans.

In order to understand what is going on in DR 3 anime[both] you need to at least know DR2 since it focuses on it's characters, what happened to them and the consequences. It sort of sets the ground for the other two anime. Then it would be good to know the basic summary of DR Zero and Despair Girls to understand a couple of episodes too. Killer Killer can be totally ignored though.

I would recommend you see let's plays of DR2 first, then look for summary of DR Zero maybe. Definitely try to look at least at the main plot of Despair Girls and who it's main characters/antagonist look like. Otherwise one episode of Future will feel really off. Then watch Future and Despair together. Like watch one episode of Future and then one episode of Despair. They where aired at the same time because the person that made the series wanted for them to be watched together. They sort of complement each other too. Despair goes quiet a bit on the background of some new characters from Future. Then once you finish watching Future and Despair watch Hope arc.

If you like the series after all that, do look forward to the new game, New Dangan Ronpa V3!~ [New cast, and new universe apparently] It comes out in Japan on January 12, so we won't really see much of it until later but still ^ ^

The direct sequel to Danganronpa The Animation is Future-arc. Despair-arc is actually a prequel to the Danganronpa 2 video game. Hope-arc (which is just one episode) serves as the final episode of both series.