  The first part of this thesis focuses on the production of thermal dileptons
from a hadronic gas at finite temperature. The rates are calculated by an
expansion in Pion density and constrained by broken chiral symmetry and vacuum
correlation functions, many of which have been measured by experiment. We focus
on emission processes having two Pions in the final state.
  Next, follows a separate discussion on viscous hydrodynamics and its effect
on $p_\perp$ spectra and elliptic flow. A non-central hydrodynamic model of
Au-Au collisions in 2+1 dimensions is simulated.Off-equilibrium corrections to
the distribution can bring about large changes in the differential elliptic
flow, especially at higher $p_\perp$. Also discussed is the shear viscous
correction to dilepton production in a quark-gluon plasma (QGP) emanating from
$q\overline{q}$ annihilation in the Born approximation. It is argued that a
thermal description is reliable for invariant masses less than $M_{max} \approx
(2\tau_0 T_0^2)/(\eta/s)$. Shear viscosity leads to qualitative differences in
dilepton $p_\perp$ spectrum, which could be used to extract information on the
thermalization time, viscosity to entropy ratio and possibly the thermalization
mechanism in heavy-ion collisions.
  Finally, the dilepton rates used in this work are integrated over the
space-time evolution of the collision region and compared to the recent results
from the NA60 experiment at CERN and the PHENIX experiment at RHIC. The role
played by chiral symmetry restoration in the hadronic phase and viscosity in
the QGP phase is discussed.
