The Signal protocol is designed for secure, private, encrypted messaging and real-time calling. The protocol, designed by Open Whisper Systems, is used in an increasingly large range of tools (including by Facebook and Google), but their own app is the most interesting application of it. 

The (open, GPL) Signal app is a secure, private messaging and voice chat app for iOS and Android, offering guaranteed and strong end-to-end encryption without having to sign up for a service with dubious privacy standards or further agendas (e.g. Facebook, Apple, Google, Whatsapp, Viber etc). No ads, no account details kept by the company, no means for them (or anyone) to store or intercept messages or calls, the organization is funded by donations and grants. The app uses your phonebook to discover other contacts using Signal - I don't have many yet, but hopefully a few of my contacts will see this and install it. Call quality seems excellent - as good as Skype used to be before Microsoft maimed it - though I haven't used it enough yet to assess its reliability. One disadvantage is that, if you have more than one phone and phone number, there seems to be no obvious way to link them together. That's a particular nuisance on a dual-SIM phone.

It needs a real, verified phone number to get started but, once you have done that, you can link it to other devices too, including PCs (via Chrome or a Chrome-based browser like the excellent Vivaldi), using a simple QR code (no accounts!) so this is a potentially great replacement for things like Whatsapp, Skype, Allo, Viber, etc. No video calling yet, though you can send video messages (and most other things).