In this talk I will first review some basic facts on Brill-Nother loci
of line bundles on a smooth, projective curve C of genus g, with general moduli and their interplay with geometric information on C.

Then, I will remind some similarities and some differences for (semi)stable, rank-two, special vector bundles on C, and finally
I will report on the approach used,
in the recent joint work with C. Ciliberto arXiv:1312.6239