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.