You can browse the list of listings from the "Listings / Manage listings" page in your Admin panel. From there, you can monitor the listing activity in your marketplace.
All the listings in your marketplace will appear in that section. You can find the:
author (and access their profile)
date it was created
date it was last modified
category it belongs to
status (open or closed)
You can also easily access the edit page if you want to update something in that listing.
Finally, you can sort the listing by creation date or last updated date to easily manage them.