  In the last few years several dualities were found between the low-energy
behaviors of Chern-Simons-matter theories with unitary gauge groups coupled to
scalars, and similar theories coupled to fermions. In this paper we generalize
those dualities to orthogonal and symplectic gauge groups. In particular, we
conjecture dualities between $SO(N)_k$ Chern-Simons theories coupled to $N_f$
real scalars in the fundamental representation, and $SO(k)_{-N+N_f/2}$ coupled
to $N_f$ real (Majorana) fermions in the fundamental. For $N_f=0$ these are
just level-rank dualities of pure Chern-Simons theories, whose precise form we
clarify. They lead us to propose new gapped boundary states of topological
insulators and superconductors. For $k=1$ we get an interesting low-energy
duality between $N_f$ free Majorana fermions and an $SO(N)_1$ Chern-Simons
theory coupled to $N_f$ scalar fields (with $N_f \leq N-2$).
