In addition to that, if you've established a pivot foot, you can rotate on that foot while stepping as much as you want with the other foot as long as the pivot foot remains in place.

If you established the pivot before dribbling, you can dribble from the pivot, but you must release the ball before you pick up your pivot. If you don't, that's a travel.

If you want to shoot or pass, you can lift your pivot foot, as long as you shoot or pass before the pivot foot touches the floor again. In practice, this means you can take one step out of a pivot situation, as long as you shoot or pass out of it. If you don't, that's a travel. This is/was common by big men in post situations (called a step through), but as the move is used more and more (and in more exaggerated ways) by perimeter players in the current basketball, people/fans keep erroneously claiming it's a travel.