My house was built in 1986 (It is v. v. Cosby Show era) and the grout is original. It also hasn't been subject to anything to try and remove the grotty color in that time either.
So the grout looks black. Mainly.
I sat down with a magic eraser. It works really well, but requires a lot of elbow grease. I have a big country kitchen, a breakfast nook and an entry way to do.
I tried a bleach pen. This worked just as well and required no elbow grease.
Hmm, the cost of enough bleach pens to do this amount of floors. . .
SO I got out the hydrogen peroxide and poured it straight on. A bit better, but not as good as the bleach pen.
I put on my thinking cap and got out the clorox bottle. Poured some bleach directly on it.
It worked beautifully. Stinks like a demon, but it WORKS.
Tomorrow I am going to try Oxi-Clean and see what that does. I'll report my findings if anyone is interested.
I think, based on my experience with the fumes, that I will mentally split up my tile floors into about 10 small areas, then one at a time, clean the grout with bleach. Between each cleaning, I can let the fumes air out for a while. After I'm done, I'll steam the floor to get all the bleach up.