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I set out to find just some basic information about how text messages translate into website actions, and ended up with more information than expected. SMS is the term for short messages service, referring to a message being up to 160 characters, and being sent from a mobile phone, or (SME) to a short messages service center, (SMSC), stored, and then forwarded to another SME.

A good diagram would be here, including a few other paths an SMS can make, but also beyond the scope of what I sought to find.
http://www.wirelessdevnet.com/channels/sms/features/sms.html

The relevant part would be the SMSC, or SMC, or GSMC, or LOL, and JK. The GSMC, or gateway short message center would simply receive the messages, rather than forward them. To my surprise this could be as simple as a mobile phone and desktop application. Then arises two questions, how intense does my phone-web application have to be? Do I want open source or not?

The popular open source application to integrate with a GSM modem is Kannel.

http://www.kannel.org/overview.shtml

It was pretty easy to download a release, unpack, configure and make this on Ubuntu. I do not have a compatible GSM modem however so a complete test wasn't possible. I had hoped to use an iphone, but upon reading multiple sources this is not a possibility.

And more user-friendly approach would be Ozeki, http://www.ozeki.hu/

This enables use of bluetooth and usb connections between your GSM enabled mobile device, and your SMS gateway application, (Ozeki in this case).