Well, this does involve a bit of hands and knees scrubbing, but it works. If you buy an electric scrub brush (a small round one, that rotates around in a circle ---I think it is called the Sonic Scrubber or something like that) it eliminates some of the scrubbing and works really well. (You can buy it at Target or Walmart) Use a gel bleach product...clorox or comet both make them. Squeeze it on the grout, a small section at a time, let it sit a few minutes, and then scrub with the electric brush. Then you have to rinse with clean water. It's a lot of work, but really does the job. I usually only do this type of scrubbing once a year.