From the Manage your Apple Card account Apple Support document:

Apple Card is currently available only to customers participating in the Apple Card Preview.

A reminder, this is still Apple Card Preview times. Somewhat like a beta, but with more legal obligations. So if you are not getting the card invite, have patience. Some people are really getting riled up over this. Speaks to the compelling nature of both Apple Card and the ecosystem.

Credit limit increases are not currently supported.

If you tap the “…” button, then scroll to “Credit Details”, you’ll see your credit limit. Given that the vast majority of credit cards offer some mechanism to bump your credit limit, I’d expect this to change. Again, this is a beta period.

Only the account owner can currently use Apple Card. If a family member or friends wants to use Apple Card they will need to apply for Apple Card.

This last one is interesting. There’s an implication that you’ll be able to allow future Apple Cards for family members and friends, tied to your Apple ID. Lots of credit cards allow this as well. A great way to introduce your kids to the responsibilities and mechanics of credit cards.

I wonder if we’ll eventually see a business version of Apple Card.