UV rays through glass

Just a quick query about ultra-violet-rays-through-glass.

I had understood that one couldn’t “burn” through a window, because (normal) glass filtered out the UV rays. Likewise through a plastic window.

However when you buy sunglasses, more expensive ones come with UVA/UVB filter stickers, highlighting their greater protection.

So what comes through glass and what doesn’t come through glass, what is actually damaging or not, and why would you need a special type of glass or plastic for your sunshades to block UV?

from http://www.sciencenet.org.uk/database/Physics/9812/p01347d.html

"Normal glass (as used in windows) is transparent to UV radiation up to a wavelength of about 330nm (or UV-A light). The transparency is quite high so almost all UV-A light will pass through glass. Beyond 330nm (UV-B and UV-C) almost 100% is stopped. "

note that UV-A is still dangerous!

Cecil Adams on which UV does and does not pass through glass .