In skateboarding this can be done with certain tricks for extra style\points. It is, essentially, in the same context as a tweak (though it is a different procedure). The following is the how and when inverts can be executed:
1. In plants, namely Mute Inverts. As you grab your board bend your knees back and push out your chest and stomach (very hard to do in a plant).
2. In a grab. Any grab on the side of the board can be inverted (excludes nose grabs, tail grabs, rocket airs etc.). The execution is basically the same as a plant invert, though there is no set way. The wackier and more inventive the more style/higher the points.
3. In grinds. An inverted grind is different to the others in the sense you do not grab your board. You can mix it up anyway by crossing your feet, leaning back or forward, having one foot's toes hanging over the edge and the other's heel over the edge... basically anything you can think of. This is predominantly a freestyle trick.