This style is prevalent throughout the English-speaking world, though it is by no means universal.
Despite the names, choice of knitting style has nothing to do with the handedness of the knitter.
Various non-Western styles also exist, many of which are substantially similar to these, but which twist each stitch, making for a subtly different-looking fabric.
The yarn is wrapped around the right hand for tension (in one method, the tail of the yarn is wrapped around the little finger of the right hand for tension, and over the index finger for control—see illustration).
The right hand will hold the needle with the most recently knit stitches.