Is homebrewing beer legal?

The answer:  Yes, though there are limits, which depends on what you're doing with your brew, and what state's law applies.
Article here.

Brief overview: home brewing was affected by Prohibition in 1919 (passage of the 18th Amendment), which outlawed alcohol. When the 21st Amendment was passed, home brewing of beer was not part of the repealed Amendment in 1933 (although wine making was). It wasn't until 1978 that President Jimmy Carter signed H.R. 1337, which contained an amendment sponsored by Senator Alan Cranston creating an exemption from taxation for beer brewed at home for personal or family use