Why do I only get iPhone text messages?

I have the iPhone 5. My friends have told me recently that they have been texting me (non-iphone users) and that I never reply. The problem is, I never get anything. It seems now as if the only people I get messages from are from iPhone users. I have played around in the settings and everything seems to be normal, I have even turned off/on my phone. Any ideas on how to fix this? Thanks.

Added (1). @Zoe: IMessage is on, yes. Is it supposed to be off?

Is your Imessage on? They can only be sent between iphone users. To check you go on settings, messages and imessage.

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