imessages

iPhone: Settings > Messages > Send & Receive. Does it say, "Use Your Apple ID for iMessage?" If so, tap on that and SIGN-IN.

Settings > Messages. Ensure that MMS and Send as SMS are also enabled.

Settings > Your Name > iCloud. Messages in iCloud = ON.

Mac: Messages > Preferences > iMessage. Sign-in to the SAME Apple ID used are signed in at (Send & Receive) on the iPhone.

Also, ensure that your iPhone and Mac are both up to date on iOS and macOS.

If you are asking about Apple Messages app/application, have you signed into Messages to see if you can see them there?

The computer.