What makes glass monitors different from matte or glossy?

"Generally, glossy screens have better color contrast at the cost of increased glare. Newer, better glossy screens (like Sony VAIO Z) try to reduce glare while keeping the brilliant contrast.

I've heard a lot of people say to get a monitor with a glass front.

All I have seen are basically transparent plastics. Probably they mean ""glossy.""
Update: apparently, there are some glossy displays (like the new iMac) that use glass as the exterior coating material. I'm not sure if the glass is an extra layer of coating or it's the LCD coating but anyway, it doesn't really matter what they are using for manufacturing. You should really compare picture qualities. The new glass displays might provide a better quality. And by the way, glass displays are not matte.

What are the advantages? Is it more expensive?

Crisp pictures. No, the cost should be similar. Some manufacturers might choose to provide one kind only. Others might choose to charge (a small amount) more for a kind but the manufacturing cost shouldn't be different.

What laptop screens have glass monitors?

Most laptops currently on market feature ""glossy"" (not glass) screens by default. I don't know the glass ones but it should be visible in their marketing materials."

Try one before you buy!!! Don't only check it out in the store you need to check it out near a window. The glare is a deal breaker for me! I borrowed a friends to try it out and I didn't even use it a whole day. If you will be using it anywhere you cannot control the lighting it's aggravating at best.