Reddit reviews Reef Fish Identification - Florida Caribbean Bahamas - 4th Edition (Reef Set)

Don't know of a great app, but there are lots of great books on the subject. They are all location-specific, so recommendations may be based on where you dive.

For the Caribbean, I can highly recommend this book:

Reef Fish Identification - Florida Caribbean Bahamas - 4th Edition (Reef Set)
https://www.amazon.com/dp/1878348574/

It is part of a set that includes books on fish identification, other creature identification, coral identification, and then a book on fish behavior.

This is THE book.

I have it from diving. My girlfriend has an abridged waterproof copy that's printed on synthetic paper that she has actually taken on dives with her.

You can also buy a 3 volume set that includes coral and other reef creatures.

Edit: I just looked at mine. It's great but it talks more about how the fish will respond to divers. I don't see much help on whether or not they're tasty.

Sure thing. These are my favorite guides.
Pretty exhaustive, good details on habitat, color, and range, and lots of pictures of different phases and regional color morphs.

https://www.amazon.com/Reef-Fish-Identification-Florida-Caribbean/dp/1878348574/ref=sr_1_2?ie=UTF8&qid=1550494892&sr=8-2&keywords=caribbean+reef+fish+book

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It's a lot more fun if you do it yourself, and you learn more.

I really liked this book, and it's counterparts. This one has all the related books in the "users also bought section"

Reef Fish Identification - Florida Caribbean Bahamas - 4th Edition (Reef Set) https://www.amazon.com/dp/1878348574/ref=cm_sw_r_other_apa_gkowxbSEPQ258

It's got full color pictures of fish, and a bit of information on them. It's also easy to search for what you saw, and if you want more info, it can give you a name to Wikipedia.