An extensive review of literature simulations of quiescent polymer melts is given, considering results that test aspects of the Rouse model in the melt. We focus on Rouse model predictions for the mean-square amplitudes〈(Xp(0))2〉and time correlation functions〈Xp(0)Xp(t)〉of the Rouse modeXp(t). The simulations conclusively demonstrate that the Rouse model is invalid in polymer melts. In particular, and contrary to the Rouse model, (i) mean-square Rouse mode amplitudes〈(Xp(0))2〉do not scale assin−2(pπ/2N),Nbeing the number of beads in the polymer. For smallp(say,p≤3)〈(Xp(0))2〉scales withpasp−2; for largerp, it scales asp−3. (ii) Rouse mode time correlation functions〈Xp(t)Xp(0)〉do not decay with time as exponentials; they instead decay as stretched exponentialsexp(−αtβ).βdepends onp, typically with a minimum nearN/2orN/4. (iii) Polymer bead displacements are not described by independent Gaussian random processes. (iv) Forp≠q,〈Xp(t)Xq(0)〉is sometimes non-zero. (v) The response of a polymer coil to a shear flow is a rotation, not the affine deformation predicted by Rouse. We also briefly consider the Kirkwood–Riseman polymer model.