Some of my phone messages do not come to my computer, only my iPhone. These are messages from people in my contacts. I have the settings enabled to block spam, but none others.
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On your computer, open iMessage.
Under messages menu -> Preferences -> iMessage, ensure enable messages in iCloud is checked. Make sure your phone has comparable settings.
Set up Messages on iPhone - Apple Support
Make sure both are logged into the same iCloud account.
After getting a new iPad, I no longer got messages from Android users on the iPad. I saw recommendations online to use “text message forwarding” but that option did not exist on my iPhone. I noticed that the new iPad had chosen to start new conversations from my iCloud email account rather than my phone number. By setting my MBP, iPad, and iPhone to start new messages from my phone number (in the settings of the Messages apps), the “text message forwarding” option appeared in the Messages settings on my iPhone. I then added the new iPad and older MBP to the list of devices behind that forwarding option. It all seems to work now.
There's also this: Set up iPhone to get SMS messages on Mac - Apple Support
Text message forwarding is not working on my MacBook Air
