To clean grout, we usually use a steam cleaner. Its slow but does a great job. We have only ever done floors and not wall tile grout. - Probably because it hardly gets dirty except for the exceptional filthy commercial premises or house.
We did try something new yesterday on floor grout that we were asked to clean. The grout was black due to the amount of dirt.
After we had finished it was white. Client very impressed and so were we.
We purchased some grout cleaning brushes. - they are stiff pointed brushes that run along the grout lines. Makes the job very easy.
To clean, the chemical we used was UBIK2000. We then mopped up and wipes the grout and tiles clean.
You can use an acidic solution or bleach - there were a few spots we did use bleach where there was staining to the grout and it worked.
Hope this helps. - there are other guys here that have plenty more experience than me so maybe someone might even give you a useful tip.
All the best
Dave