• Lollipop has adaptive brightness which can be turned off or on in the settings menu within display tab (which is a battery drainer for me personally and prefer to keep it off).
  • Search in settings is much awaited feature, that we have finally got..!
  • View you data usage of cellular network by tapping on cellular symbol (for mobiles)
  • Now long pressing a notification reveals the app that is pushing the notification.
  • Smart Lock is another often overlooked feature-from-heaven for those of us who make use of Bluetooth gadgets or NFC tags. For example, if your smartphone regularly connects to a Bluetooth device (like your smartwatch, car, stereo), you can make it a trusted device in Android Lollipop. This will remove the security challenge when unlocking the device even if one is set-up. Especially handy in the car, where you want to spend as little time fumbling with your docked phone.
  • You can "pin" apps so that whoever ends up using your phone is confined to that one app. In order to escape, one would have to press both the recents and back key simultaneously and then go through your security challenge.
  • Lollipop device will actually keep the apps that were running in the background before and after a reboot within your Recents/Multitasking tab (they're not powered in case you're wondering). 
  • The ability to turn on wifi, aeroplane mode etc from quick launch shortcuts menu by just tapping on the symbol rather than the long press that was necessary to do the same in kitkat is quite handy or you can also go into the wifi setting by simply tapping on the text wifi below the symbol.
  • a two finger swipe down reveals the notifications+quick launch shortcuts at once.whereas a single finger swipe down once reveals notifications only and single finger swipe down once again reveals quick launch shorcuts along with the already present notifications
  • screen recording in lollipop is an inbuilt feature and thereby doesnt require you to connect the device to computer or root your device for recording it just requires you to download an app from playstore.
  • Now you get the notifications from your lockscreen even if you have a passcode and allows you to select whether you want all notifications displayed or want to hide sensitive contents from notifications which hides notification contents from selected apps like whatsapp and replaces its contents in lock screen with a phrase "contents hidden" thereby enabling you to see which all apps have notifications for you even without unlocking your device!!pretty handy (U can also altogether ban notification from appearing in lock screen from within settings)
  • whenever you get a new notification it appears as a banner which you you can push left or right to dismiss so that you dont have to move your thoughts out of what you are doing at that time...!