Read-only feature:

Invite the character to your campsite and, eventually, to move to your island / Invite the character for photo shoots at Photopia / Unlock a special poster of the character / Invite character to the Roost for a cup of coffee / Invite character to Happy Home Paradise to design their vacation home

In short: Any non-SP card from Animal Crossing Card Series 1, 2, 3, 4, 5, Promos, New Leaf Welcome, or (as of the March 2021 update) Sanrio.

One character can be invited to the campsite per day.

After scanning at Photopia, the character's poster will be available in the Nook Shopping catalog.

The Roost and Happy Home Paradise functionality added in November 5, 2021 update. Happy Home Paradise is paid DLC.


Read-only feature:

Invite the character for photo shoots at Photopia / Unlock a special poster of the character / Invite character to the Roost for a cup of coffee / Invite character to Happy Home Paradise to design their vacation home

After scanning at Photopia, the character's poster will be available in the Nook Shopping catalog.

Special characters generally become available for photo shoots when their model is added in an update. For example, Jack became available along with the Fall update on September 30, 2020.

Some currently-poster-only characters (next feature down) are expected to made available as Photopia models in future updates. DJ KK (listed under this feature) is not yet available but has been specifically given as an example of a future addition in a Nintendo Direct (video).

The Roost and Happy Home Paradise functionality added in November 5, 2021 update. Happy Home Paradise is paid DLC.


Read-only feature:

Unlock a special poster of the character

After attempting to scan at Photopia, the character's poster will be available in the Nook Shopping catalog.

Sources: Nintendo's official Japanese website: Features, Compatibility table / GameXplain (video) / @Walrus_McCloud on Twitter (4/22/2020 additions), u/dingycollar on Reddit (Luna addition 7/30/2020), JayBee & Milly on YouTube (video) (Franklin and Jingle addition 11/18/2020)