Adult Reception only?

Depends on how you're defining adult.
18+ write "adults only please" on your invitation.
If you're looking for more of an alcohol based night and want it 21+ you can write 21+ only on the invites.

You don’t put it on the invitation. Address your invitations to only those invited - ‘Jane and John Smith’ rather than ‘the Smith Family’ and you could also get RSVP cards which say ‘we have reserved x seats in your honour’ or ‘__ of x attending’ where you fill in x with the number you’re inviting.

Don’t invite kids. Simple.

Yes. Put it on the invitation.
The whole not addressing the invite to the children does not work in my area.

View Quoted Comment Also a good point. Many bride's on here report that addressing the parents only often doesn't work or that they'll ignore it. You have to be kind of blunt about it or people will either genuinely not know or play dumb.
Personally I probably wouldn't have thought that the kids not being addressed on the envelope meant they weren't invited either. 🤷

I put it on my website & on the invite I put x amt of adults will be attending.

I will be putting “Adults only” on my invites and on the website... I’m also allowing one of my bridesmaids to bring her infant. My little brother in law and my FH nephew will be allowed only... so 3 total... but they know they are the only ones allowed so there will be no confusion once they get the invites..

I put Adults only reception to follow at the bottom of the invitations. Then I put on the info card no children under the age of 21 except those in the bridal party

People say don't address the invite to include kids but I feel like nothing is really wrongggg with explicitly saying we love kids but for our wedding it is adults only, make it a date night.