And what will happen if I eat them after they're past the expiry date?
All of the answers you are looking for have been touched on in various parts of this question: How long can I keep eggs in the refrigerator?
As with just about every other food, you're better off interpreting the sell-by or best-before dates as a conservative guideline; any food can go off before the date if it's been damaged or mis-handled, and many foods will still be fine long after they "expire". StillTasty.com is a good resource for finding out how long various foods actually last in storage.
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The sell by date isn't so much going bad (bad eggs are rather obvious) but Salmonella.
Most eggs, especially factory farmed, have traces of salmonella on them - it can pass through the shell. But unless you are already ill you can handle it, the older the are the longer the bug has add to get into the egg and grow.