How to block spam messages on my iPhone?

We'd all love to find a great way to block spam messages. Unfortunately, as you've learned, they come from different numbers, even if the message is the same. You can block each number individually, but there really is no way to completely block spammers. Apple doesn't deliver the messages. Your carrier does. Check with your carrier to see what they may offer in the form of spam filtering.

You can enable filter unknown senders in settings>messages, or block a single message in the Message app

Open the Messages app, in the Messages conversation, tap the name or number at the top of the conversation,

tap Info in the top menu, then scroll down and tap Block this Caller.

But there isn't much you can do as lobsterghost1 just explained you

Yes, you can filter unknown senders. But I didn't mention it, because I've missed messages from for example a doctor or a service I didn't want to miss. The reality is, spammers are creative, annoying and most difficult to get rid of.

You should be offered the option, when you delete the message to mark it as junk. As I understand it, that information gets reported to carriers who can take action. It doesn't block the message but it may help, in the aggregate, to cut down on them.

Won’t do you much good though reporting it as junk. I get these text messages multiple times a day, EVERY DAY. Neither the phone carrier (AT&T) or Apple, has or will do, anything about it. Ever!