A very standard question with very standard search results, just wanted your input as well. My situation is close to the stock picture, but I will focus on removal in the grout areas. I am planning on bleach plus toothbrushes, but I want to be careful not to attack the grout itself too much, just get rid of the stuff on top.
It occurs to me that creating a sort of bleach-based paste might be good. Any solid material I could mix with the bleach? One video suggested something along those lines.
I also find it interesting how the treatments suggest either something very basic (bleach) and alternately suggest very acidic materials (vinegar), possibly for different phases in the treatment. It's like the Andromeda Strain! Curious for what you've found effective.