Facebook took another step to becoming the defacto operating system of the web 2.0 world. Though currently in beta they released a JavaScript Client Library for the Facebook API. What does that mean? It means that the 13,000+ Facebook applications that are currently hostable only inside www.facebook.com can now have a presence on the rest of the world wide web.
How does it work? The key to a Facebook application is getting access to the underlying Facebook object and User ID for any given Facebook member. This usually is given to an application directly by Facebook when the user clicks on the application from within their Facebook profile page.
The JavaScript API attempts to login as the current browsing user. If the user already has a valid Facebook session available everything just works. If not the user is presented the following friendly dialog to log in to the application:

The connection to Facebook is made from the user's browser. The hosting site does not get access to Facebook credentials at anytime.
There are a few limitations on the applications that wish to support this. They must be IFrame applications. They also have to deal with a different set of information than the traditional rich Facebook POST variables. I will have more information and an example up here shortly.
You can read the blog posting here: Facebook Blog- Facebook JavaScript API
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