Many swear by citric acid: according to reports, a solution of water and citric acid applied to the affected grout, left to work briefly, then cleaned with a brush and rinsed with clear water is enough. The result: visible cleanliness and a fresher indoor climate.
A mixture of baking soda and water helps with vigorous scrubbing, while vinegar water cleans and disinfects additionally. What's important afterwards is to thoroughly dry the grout, as moisture is the breeding ground for new growth.