What is the compounds in bleach?

Bleaches often contain chlorine, though it's not an absolute requirement; hydrogen peroxide and ozone are also pretty effective bleaching agents and are sometimes used in commercial operations (they're somewhat difficult to handle and not particularly suitable for home use). The most common liquid bleach (at least in the US; it may be different in other countries) is a solution of sodium hypochlorite (NaClO) in water.