When we were children, we saw magicians do extraordinary things with a flick of the hand. Possibly taking inspiration from such things, the S4 features the Air Gesture.
One can direct the phone to do certain things with a flick of the palm; for example, answering a call or scrolling up or down a website. The feature needs to be "trained".
It did "train", only, unlike a pet, it seems to have several masters.
I had some embarrassing moments at one of my edit meetings when a simple gesture of keeping down his pen by my colleague resulted in the webpage I was reading out from scrolling up. Another "airy" feature is Air View that previews content, say from an album.
The S4 features Smart Pause, where a video pauses when you look away from the screen and starts playing again when you look back. Again, this feature worked, but not always.
One feature we found useful was the S4 tracking our eye movement as we looked up or down the screen and scrolling the web page.
Samsung gives you personal cloud storage of 1 TB with HomeSync, where you can store photos and the like. It can also be accessed on the bigger screen with a simple URL, with the S4 doubling up as a mouse.
The WatchON feature can download electronic programme guides and act as a remote for TVs or set-top boxes.
A feature which impressed us was the S Translator. The S4 also bundles in S Health.