This is a recent innovation introduced (by film and TV) from the States. It is however a good way to break the ice before the wedding if your two families haven’t met ‘en bloc’.
A supper at your venue (or elsewhere if you are saving the ‘impact’) is a nice way to start the festivities. Traditionally speaking, it happens the night before your wedding and is usually an early evening affair, meaning your guests won't need to take any extra time off work during the day and you still have time to disappear with your bridal party for some last minute pampering! That being said, it can also take place a couple of days in advance to allow for a little more rest and recuperation before the main event. Its novel introduction on the wedding scene means the etiquette can be fixed to suit your aspirations.
It provides a wonderful opportunity for your closest friends, family and future in-laws to get to know each other in a much more relaxed environment and celebrate the impending nuptials in an intimate setting - realistically, they're probably not going to be able to spend that much time with you on the day.
If you're sticking with tradition, the Groom's parents are usually the hosts of the rehearsal dinner and will take full responsibility for the organisation (and cost!) ... this does also mean the guest list is usually subject to their approval. At the very least this should include the immediate family, bridal party and their partners. Generally the celebrant or officiant will attend (you really should invite them...) and people who have travelled a distance will be included although, as already suggested, it doesn’t have to conform to any particular format.
On the other hand, if you are going for a fancy affair with larger guest numbers in a hotel or country club, you’d be wise in sending out official invitations as you’ll want RSVPs for catering. Send these out with or shortly after your wedding invitations to help everyone keep on top of their schedules.