My iPhone says I’m connected to Wi-Fi. It does not say no internet but I still don’t have internet. Any ideas?

If you've already tried (to no avail) all the steps provided in this support article:--> If your iPhone or iPad won't connect to a Wi-Fi network - Apple Support and the issue persists, does it only happen at home or with all Wifi networks?

Should be the former, the issue must be sought in your modem-router configuration (try to restart your modem router, wait for its complete autoconfiguration, then test the connection again). If the issue persists, see also this support article:--> Recommended settings for Wi-Fi routers and access points - Apple Support

Should be the latter, try resetting your network settings in:

Settings>General>Transfer or Reset [Device]>Reset> Reset Network Settings. Bear in mind that this procedure also resets Wi-Fi networks and passwords, cellular settings, and VPN and APN settings that you've used before, but NO other data is affected. When done, restart your iPhone and test it.

If the issue still persists, contact Apple support directly using this link:--> Get Support or make an appointment (*) and have your device inspected at an Apple Store or AASP (Apple Authorized Service Provider) among this list:--> Apple – Location Selector. After checking it out, they'll give you all the available options.

Regards

Giulio

(*) You can do it:

• Online:--> Genius Bar Reservation and Apple Support Options - Apple;
• Contacting a local Apple Store or AASP among the list provided above;
• Using the "Apple Store" app, available and downloadable from AppStore.