Braverman and Kappeler introduced a refinement of the
Ray-Singer analytic torsion associated to a flat vector bundle over a
closed odd-dimensional manifold. We study this notion and improve the
Braverman-Kappeler theorem comparing the refined analytic torsion with
the Farber-Turaev refinement of the combinatorial torsion. Using this
result we establish, modulo sign, the Burghelea-Haller conjecture,
comparing their complex analytic torsion with the Farber-Turaev
torsion in the case when the flat connection can be deformed in the
space of flat connections to a Hermitian connection. We then compute
the refined analytic torsion of lens spaces and answer some of the
questions posed in [BK1, Remark 14.9].