Apple's iPhone uses two major messaging systems, standard SMS texting as well as their own iMessage, the latter works when the phone has an internet connection, which, given how most phone contracts are geared towards high data consumption, will act as your primary messenger. Alongside this, you have FaceTime, the app which allows you to video call/chat with fellow iPhone users also using 4g or WiFi. The fact that both use data means that it is likely if you experience a problem with one, you will soon find that there is a problem with the other.
Messages Aren't Delivered
Often times when using iMessage you will see that your message hasn't been delivered, accompanying this will be a red exclamation mark adjacent to your message. This is generally due to a brief iCloud outage which can easily be solved by going to your settings and re-logging into iCloud. However, it may also be due to lack of data which can be solved by tapping on the aforementioned exclamation mark and sending the message via SMS.
Unable To Recieve And Make Calls Through FaceTime
To begin with, you should just check that the app or phone itself doesn't require an update, as this is the easiest problem to resolve. FaceTime can be somewhat temperamental if you are using an older iOS or OS X. This problem may also apply to the user on the other end of the line. It is also possible you or the person on the other end have lost internet connection, or your connection is not strong enough, or even that your date/time is incorrect.
FaceTime or iMessage are stuck trying to activate
One of the strangest (yet surprisingly common) error messages on FaceTime reads: "Could not sign in. Please check your network connection and try again." Similarly, if you check under Settings > Messages you might see a "Waiting for activation..." notice. This can be a major problem which will require a somewhat drastic fix:
Visit Settings > FaceTime and tap your Apple ID.
Tap Change Location and ensure the correct country is activated.
Follow the same procedure under Settings > Messages > Send & Receive.
Make sure you are logged in to the respective services with the correct password.
Then, reset your device by holding the home and power buttons down simultaneously.
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