Do event registrations require approvals?

Rachel Jackson , You are correct, the no RSVP will confirm the registration without needing approval. 

Thank you this is helpful! Tom Paolucci If you select "invitation only" as the event registration option, will the event only display on the group's calendar for those who were specifically invited, or will it still be visible to all users and have some sort of warning/note that the event is by invitation only? I am trying to test it in our dev environment, so looking to confirm.

Registration type does control the visibility of events, they are all always visible.  

I think Patrick M. meant 'doesn't control visibility of events'. Anyone can see the event, but only invitees will be presented the Register button. Those who have not been invited would not see an option to register. There is not a message or warning that it is an invitation only event. If that's desired it would have to be added to the description for the event.