Hi there,
You can set the date filter in the [tribe_events] shortcode to a date as far back in the past as you want, and the shortcode will output events from that date forward (including upcoming events). There is not currently a shortcode to display only past events, but there is a past events page created by default: yoursite.com/events/past.
Alternatively, you could pull a custom list of events with the tribe_get_events function.
Please let me know if you have any questions!
Thanks,
Jennifer