You'd like to hear a sound, see a badge or read an alert on your computer when important news breaks, a friend challenges you to a game or tickets to the next big sports or music event go on sale. If you've granted permission for various applications to notify you, but don't receive their alerts, don't worry yet. Unless your device is hacked or jailbroken, the solution may lie in tweaking a setting or relaunching an app.
Double-check your device's setting. Tap "Settings," "Notifications," and then toggle the main notifications bar "On." If this setting is turned "Off," you will not receive notifications from any app, regardless of your app-specific instructions.
Check the settings of individual apps listed under the main notification bar to make sure their sound, alert and badge notifications are switched "On," as you desired. You may have inadvertently prohibited notifications when you originally launched these apps.
Reactivate notifications if you've recently restored your iPhone, especially a new one, from a backup. Open each app at least once to grant fresh permissions. Again, double-check that your main notifications setting is turned "On."
Your Wi-Fi firewall may be blocking port 5223. For notifications to work, this port must allow TCP traffic to flow through. Consult your home Wi-Fi system manual or network administrator to inspect and reconfigure your firewall as needed.
Jailbreaking an iPhone considerably disrupts push notifications and other services. Apple warns of this instability on devices whose operating systems have been hacked.
A couple of free apps can help you assess your device's push notification performance. iPusher tests for any "clogged arteries" on your router or iPhone. iPushTest examines your push response time; if you receive a response in less than two seconds, then your push notifications are probably working correctly. If not, or if other issues persist, contact Apple support.