A good description of eclipsing binaries can be found here.
One of the slickest presentations of eclipsing binary stars I have seen can be found here. Play around with the controlling variables to get a really good visualization of what makes eclipsing binaries what they are.
Some of these objects transfer mass between the stars. A description of this, with a movie simulating this can be found here. Just read the description, and scroll to the bottom of the linked page.
Eclipsing binaries in which mass transfer takes place can be classified as cataclysmic variables as well. A discussion of these variables can be found here and here on this site, and here offsite. A definitive catalog and atlas of cataclysmic variables can be found here.
Whether mass transfer takes place or not depends on the geometery of the binary system. A comment about this process can be found here.
Groups actively measuring eclipsing binary star systems can be found here at the Eclipsing Binary Observers home page, and here at the American Association of Variable Star Observers.
I have found two sources of predictions for Eclipsing Binaries. The first is a calculator and can be found on the Eclipsing Binary Observers home page, and can be found here, or by clicking the big blue button above, and the second, a PDF source produced by the Eclipsing Binary committee of the AAVSO can be found here.
This page is evolving. At present it tells a story and links to sites that do a good job of filling in the blanks.
As time goes on I will add to this page with my own observations and other commentary as I get time.
