Barkeeper's Friend makes a glass cooktop cleaner that I've found really works well. I also use Magic Erasers in between. My cleaning lady shines it all up with Windex. Be careful not to use those green scrubbers that you use for pots and pans. They tend to scratch.

my son got my cooked on grease off using a non scratch pad and the bartenders friend and a lot of scrubbing

I have a black cook top too. My pressure canner was rough on it. I made grape jam and some of the sugar cooked on. I used the fume free oven cleaner and it helped. I was worried it would take the paint off. A couple of weeks ago I accidentally turned on the wrong burner and it cooked on the vegetable oil in my aluminum Whirly Pop popcorn maker. You don't wash them, you season the pot with oil and wipe it out after you use it. I had not wiped it out yet and so it had oil and popcorn debris in it. It turned into a nasty black hard layer in the bottom of the pot and boy did it smell horrible--like burning plastic. I poured a couple cups of ammonia in the bottom and let it set for two days. You can't believe how easy it was to finish cleaning up. I learned that trick awhile back and had never tried it out. The idea is to take your grill top and put it in a garbage bag with ammonia overnight. Apparently it works.

I helped a friend clean up a stove in a house he bought to rent out. My oh My - was that kitchen greasy I used Dawn Platinum 4x on the stove. Wipe it on and let it sit for a few minutes. It took a second application but it works well and kind to hands.