  Two microscopic theories have been proposed for the explanation of the
fractional quantum Hall effect, namely the Haldane-Halperin hierarchy theory
and the composite fermion theory. Contradictory statements have been made
regarding the relation between them, ranging from their being distinct to their
being completely equivalent. This article attempts to provide a clarification
of the issue. It is shown that the two theories postulate distinct microscopic
mechanisms for the origin of the fractional quantum Hall effect, and make
substantially different predictions that have allowed experiments to
distinguish between them.
