let $c$ be a smooth irreducible projective curve. we can consider the brill-noether locus $b(2,\omega_c,r)$ of stable rank two vector bundles with canonical determinant and at least $r$ linearly independent sections on $c$. there is a complete description of $b(2,\omega_c,r)$ when $c$ has general moduli and genus $g\leq 12$. for higher genus several basic questions like non-emptyness, irreducibility, etc, are still open. the talk will focus in these questions and some conjectures.