  Motivated by the recent results from Daya Bay, Reno and Double Chooz
Collaborations, we study the consequences of small departures from exact
$\mu-\tau$ symmetry in the neutrino sector, to accommodate a non-vanishing
value of the element $V_{e3}$ from the leptonic mixing matrix. Within the
see-saw framework, we identify simple patterns of Dirac mass matrices that lead
to approximate $\mu-\tau$ symmetric neutrino mass matrices, which are
consistent with the neutrino oscillation data and lead to non-vanishing mixing
angle $V_{e3}$ as well as precise predictions for the CP violating phases. We
also show that there is a transparent link between neutrino mixing angles and
see-saw parameters, which we further explore within the context of leptogenesis
as well as double beta decay phenomenology.
