Disable notifications for specific apps
If you're lucky, the app that's bothering you will have its own, native notification settings. The Facebook app for Android, for example, lets you toggle notifications for everything from news feed posts to new photo tags. But you can also take matters into your own hands.
Just tap Settings, Apps, tap the Downloaded tab, then tap the app you want to silence. See the "Show notifications" setting? Uncheck it, and you won't be bothered by the app again.
Find a third-party "do not disturb"-style app
To exercise a bit more control than simply silencing your entire phone or shushing all of an app's notifications, you'll need a little help from the Google Play store.
A simple search for "do not disturb" on the Play store yields dozens of results. Some of them are games, others are spam filters, and a few do little more than toggle Silent mode on and off.
What we're looking for, though, are apps that silence our phones, but on demand or on a schedule, along with a whitelist for important callers and texters.
Among the standouts: the aptly-named Do Not Disturb, which boasts a one-touch instant silence timer for anywhere from five minutes to four hours. In addition to setting a schedule for when your phone goes silent, you can select a list of contacts or Google+ friends who can call and/or text you during quiet hours. You can choose separate lists of VIPs depending on whether it's daytime and nighttime. Also impressive are options such as ascending ringtone for allowed calls, as well as the ability to disable your phone's LED alert light.
A similar app I liked is Agent, a virtual assistant that syncs with your Google calendars and silences your phone during meetings--perfect for anyone with an ever-changing work schedule. As with the Do Not Disturb app, you can pick which contacts can call or text you when your handset is in silent mode, and you can set the app to send a text to anyone whose call gets blocked. Agent can also silence your handset whenever it senses you're driving, or shut down your notifications at night after you've stopped using your phone for a certain amount of time.
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