  We review the main topics concerning Fusion Rule Algebras (FRA) of Rational
Conformal Field Theories. After an exposition of their general properties, we
examine known results on the complete classification for low number of fields
($\leq 4$). We then turn our attention to FRA's generated polynomially by one
(real) fundamental field, for which a classification is known. Attempting to
generalize this result, we describe some connections between FRA's and Graph
Theory. The possibility to get new results on the subject following this
``graph'' approach is briefly discussed.
