Voxist (Free) is a visual voicemail, a modern answering machine where each message is displayed on the screen and can be listened to independently. Apple has offered this function since the first iPhone, but as it depends on the operators, you do not necessarily benefit from it. Moreover, it is a reader at RED, the non-binding operator of SFR, who informed us of its existence. 
If you don't have the built-in feature of the iOS Phone app, you can try Voxist for modern voicemail. The app was created by a French developer and is compatible with all national operators. In the rest of the world, it is more limited: the app can be used in the United States except at Sprint, and in Canada only at the Bell operator.
Even if you have Apple's visual voicemail, Voxist keeps an interest in its advanced functions that the Cupertino company does not offer. Voicemails can be transcribed for silent reading, an English-only feature in iOS. You can even receive voice messages by email, with the transcription and the original audio.
Another function offered by Voxist which does not exist at all at Apple: the possibility of defining personalized announcements. You can save several messages and associate them with different (groups of) contacts. You can even write your voice announcement which will be transcribed automatically and using variables for the name of your interlocutor. What automatically personalize the ad, which will say for example "Hello Mr. Dupont, I'm away...".
Voxist is a free app to download and you can use it without paying for its basic functions: visual voicemail for a single phone number, ten transcriptions per month, a single personalized announcement. Two subscriptions, billed at €5 or €10 per month, allow you to lift these limits and manage up to five different numbers or even obtain transcriptions in any language (French only in the free version).
On the App Store, the app requires at least iOS 9.1 and it works on both iPhones and iPads. Voxist is also available on Google Play, for Android smartphones.