In this thesis we consider retarded thermal correlators of a thermoelectrically coupled conformal plasma with added momentum relaxation and in finite $U(1)$ density background, computed in both kinetic theory and relativistic hydrodynamics. In kinetic theory we consider the relaxation time approximation, which allows us to calculate our results analytically. We analyze the analytic structure of the two point functions in the frequency space, which characterizes the collective modes responsible for the transport of conserved quantities and relaxation of the plasma back to thermal equilibrium, in both $2+1$ and $3+1$ dimensions. We compute the transport coefficients, in particular the thermoelectric conductivities.
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