How would I make the cells, below the one that I drag, go down, making a space for insertion?
Example.
I expect it to behave like following:

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This is a pretty good implementation. Basically you have a a gesture recognizer to do a tap and hold and then pan around (the trick begin that you dont move the cell on the pan, you move a UIImageView with a snapshot of the cell)
As the cell moves, you detect which row is beneath, and move the table view’s cells accordingly (e.g. with
moveRowAtIndexPath:toIndexPath:)