Use the GD > Listings widget, block or shortcode with the author filter set to current_user. It then shows only the listings created by whoever is logged in, which is what you want on a “My listings” or account page.

[gd_listings post_type="gd_place" post_author="current_user" post_limit="10"]

In the block or widget, this setting is called Filter by author. It is in the Filters group, under the advanced settings.

The values for post_author

• current_user: listings by the logged-in visitor. Logged-out visitors see no listings.
• current_author: listings by the author of the listing being viewed. Use it on a listing details page, for example for a “More from this owner” section. On an ordinary WordPress page it shows no listings.
• A user ID such as 11: listings by that user only.
• Empty: listings from all authors.

Older guides use post_author="current". It still works, but it behaves like current_author, so on a normal page it shows nothing. Use current_user for the logged-in visitor.

Places and events on one page

Add one GD > Listings for each post type, each with its own post_type:

[gd_listings post_type="gd_place" post_author="current_user" title="My places"]
[gd_listings post_type="gd_event" post_author="current_user" title="My events"]

When the user has no listings

By default the widget shows “No listings were found matching your selection.” Tick Hide widget if no posts? (hide_if_empty="1") to show nothing at all instead. To change the wording, see How to change just one language string.

Other ways to give users their listings

The GD > Dashboard widget gives logged-in users links to their own listings, favorites and add listing forms. See also How can my users edit or delete their listings?.