  We advance the classification of fusion categories in two directions.
Firstly, we completely classify integral fusion categories -- and consequently,
semi-simple Hopf algebras -- of dimension $pq^2$, where $p$ and $q$ are
distinct primes. This case is especially interesting because it is the simplest
class of dimensions where not all integral fusion categories are
group-theoretical. Secondly, we classify a certain family of $\ZZ/3\ZZ$-graded
fusion categories, which are generalizations of the $\ZZ/2\ZZ$-graded
Tambara-Yamagami categories. Our proofs are based on the recently developed
theory of extensions of fusion categories.
