Question: iOS seems to refuse to allow me to email "long" voice memos, and I'm unaware of any way to extract them from iTunes backups of my phone. How can I retrieve entire voice memos that aren't really short?

Answer: 
There is an unclear aspect of iTunes which isn't mentioned in the other answers here.

After selecting the iPhone, iTunes (12.1.2.27) shows an *On My Device > Voice Memos* list in the sidebar. However, this list doesn't actually seem to show all the voice memos on the device(!).

In particular, newly recorded memos don't seem to show for me, although they do in the [PhoneView](http://www.ecamm.com/mac/phoneview/) app. Perhaps memos only appear in that list after the device has been synced.

So: don't try and use the *On My Device > Voice Memos* list to retrieve memos from the device. Use the solutions mentioned in the other answers here instead.
First, you don't need to download any software. 

Visit [this article](http://www.tech-recipes.com/rx/6403/iphone-transfer-voice-memos-from-iphone-to-computer/), which explains how to transfer the memo to iTunes.

> 
> 1. Dock your iPhone via USB
> 2. Click the name of your iPhone under Devices in the left column
> 3. Click the Music tab
> 4. Click the checkbox for Include voice memos
> 5. Sync your device
> 6. Your files will appear under a new Voice Memos playlist
> 
> 
> 

Then, if you want to have it play on Apple Tv or hear it from your phone and it still doesn't work, there is another trick.

Go into iTunes, hold the `Ctrl` button and click on the song/memo you've imported. Choose the "Create an AAC Version" option. It will make a copy of the song above or below the original in iTunes. Then you can play this on Apple TV or off your phone like a regular song.