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The printer connection, right now, is handled through Google Cloud Print (http://www.google.com/chrome/intl/en/p/cloudprint.html), which is, admittedly, a bit wonky: another computer, running Chrome and Windows, needs to be hooked to a printer. In the future, presumably, more printers will support Cloud Print natively (or not).

As for the cloud connection and storage, that's the same as if you were using Chrome on any computer: free up to a pretty sizable limit.