Android: One of the problems with using multiple Android devices is that dismissing notifications on one device doesn't clear them from another. Pushbullet's latest update aims to fix this by syncing notifications across all devices.
Pushbullet uses Android's notification listening service (which means this feature only works on Android 4.3 and up) to monitor all of your other apps' notifications. It then mirrors them across all your devices -- your phone, tablet, and even desktop -- and when you dismiss it from one device, it dismisses them from all of them. Just as nature intended.
The feature is in beta so it may not work perfectly just yet. To activate it, you'll need to enable "Sync my notifications" in the settings of each app you want to sync notifications on.