in this talk we discuss a classification of ribbon categories with the tensor product rules of the finite-dimensional complex representations of $so(n)$, for $n \geq 5$ and $n=3$. the equivalence class of a category with $so(n)$ fusion rules depends only on the eigenvalues of the braid operator on $x \otimes x$, where $x$ corresponds to the defining representation. the classification applies both to generic $so(n)$ tensor product rules, and to certain fusion rings having only finitely many simple objects.