Android Doze is an unsung hero, saving your battery when you're not using your phone. Third-party apps like Greenify, ForceDoze and Naptime can squeeze even more juice out of your phone, but they can do a whole lot more if you tweak them.
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Kindle Fire tablets are some of the best, cheapest Android tablets around, but they're limited to Amazon's app store, which is more than lacking compared to the thousands of apps available on the Google Play Store. With a little tweaking, though, you can run any Android app on them. You can even get the entire Google Play Store on some devices.
Windows/Mac/Linux: Google's ADB and fastboot are incredibly powerful command line tools for customising your Android phone. Up until now, these tiny tools have been bundled in the gigantic Android SDK, but Google will finally let you download these tools on their own.
Android: Android's developer options have a few handy tricks, including the ability to make Android's animations go faster. However, you can only use 0.5 normal speed or nothing (unless you want to go slower). If you want to adjust them to any speed you like, you can do so with a few simple adb commands.
Windows/Android: ADB and fastboot are two immensely powerful tools. If you're new to using them, or just want to simplify the process a bit, Universal ADB Helper can make certain tasks a snap.