It is not the easiest or most enjoyable task in the world to clean your grout. Because there is a bit to know, it is best to know everything there is to know about it before diving in headfirst. Most people would think, "I'll go buy some grout cleaning chemicals and scrub and I'll be done," but it's more complicated than that. Choosing the right brush to scrub with is almost as crucial as selecting the cleaning agent.
You should not use a brush with soft bristles that do not do anything, and you shouldn't use a brush with metal bristles that are so strong that they will literally tear apart your tile and grout. The strip brushes that are made specifically for cleaning grout are the most effective for cleaning grout.
There are tools designed to do exactly what you need them to do, just like with every DIY project. The best grout brush will have a long handle so you do not have to get down on your hands and knees and strong, long-lasting polyethylene bristles that pick up dirt and grime. Metal brushes, on the other hand, go beyond that and tear up the grouting. Ideally, you will select a brush with a V-shaped contour to the bristles so that you can get right into the grout rather than just scrubbing over it.
Additionally, you should look for strip brushes with a swiveling head—180 degrees are ideal. This is for hard-to-reach places like corners, along walls, under cabinets, and other places. Choosing the right grout cleaning brush can greatly reduce the amount of time spent cleaning and free up your time for more pressing matters.