How old do you have to be to brew beer?

The laws may differ state to state, but generally speaking you must be 18 to purchase brewing supplies in the US. Even though the age to purchase and consume alcohol is 21, when brewing beer you are actually creating wort... it's not an alcoholic beverage until it completes fermentation. As far as actually brewing it at home, I don't believe there is a specific law regarding the age, other than the examples I mentioned above.