Let M (2, L) denote the moduli space of stable vector bundles of rank 2 and determinant L of odd degree, on a smooth curve of genus g ≥ 2. Owing to the work of Mumford, Newstead, Thaddeus, King, Kirwan and several others, questions such as the generators and relations, higher rank Torelli-type theorems as well as the Hodge conjecture for the cohomology ring of M (2, L) are well understood. In this talk I will survey some of these aspects for the smooth case and discuss analogous results for the case when the underlying curve is irreducible, nodal. This is joint work with S. Basu and A. Dan.