Is there a trick to clean grout in shower?

Baking soda paste and a proper stiff grout brush gets most of it. The brush is the trick honestly, a sponge just skates over the lines. For grey that won't budge, oxygen bleach mixed with hot water, left on for 15 minutes before scrubbing. I'd go easy on vinegar or other acids, used often they slowly eat into cement grout. Once it's clean and fully dry, seal it so it stays that way.