  In this dissertation I introduce relativistic heavy ion collisions and
describe theoretical approaches to understanding them--in particular, viscous
hydrodynamic simulations and investigations of final state interactions.
  The successful ideal hydrodynamic models of the collisions at the
Relativistic Heavy Ion Collider (RHIC) were extended by performing viscous
hydrodynamic simulations. This was done by making use of the recently derived
full conformally invariant second order relativistic viscous hydrodynamic
equations. Results for multiplicity, radial flow and elliptic flow in
sqrt{s_NN}=200 GeV Au+Au RHIC collisions are presented and the range of the
ratio of shear viscosity over entropy density eta/s for which our hydrodynamic
model is consistent with experimental data is quoted.
  In addition, simulations were performed of the planned sqrt{s_NN}=5.5 TeV
Pb+Pb and sqrt{s}=14 TeV p+p collisions at the Large Hadron Collider (LHC). The
elliptic flow coefficient v_2 is predicted to be 10% larger for the Pb+Pb
collisions compared to top energy RHIC collisions, and is predicted to be
consistent with zero for proton collisions unless eta/s < 0.08.
  Finally, final state interactions were investigated within the distorted wave
emission function (DWEF) model. Work is presented on an improved understanding
of the DWEF model, and the potential effect of final state interactions in the
form of a pion optical potential on the elliptic flow coefficient v_2 was
calculated to be at the ~20% level.
