How do I block SMSs on an iPhone?
You can't do it natively, and you can't do it through an App Store app.

You'll have to jailbreak and search for a blacklist app on Cydia.

Of course you can disable SMS and/or MMS entirely on the device, but the iPhone and iOS is designed to have blocking enforced from the cell carrier and not the device. Until and unless your local carrier offers an iOS app so that you can self-block addresses, you'll need to modify iOS by jailbreaking to have SMS suppressed once they reach the iPhone hardware and software.