Spin-1 hadrons have additional structure functions not present for spin 1/2 hadrons. These could probe novel aspects of hadron structure and QCD dynamics. For the deuteron, the tensor structure function $b_1$ inherently mixes quark and nuclear degrees of freedom. These proceedings discuss two standard convolution models applied to calculations of the deuteron $b_1$ structure functions. We find large differences with the existing HERMES data and other convolution model calculations. This leaves room for non-standard contributions to $b_1$ in the deuteron. We also discuss the influence of higher twist nuclear effects in the model calculations and data extraction at kinematics covered in HERMES and Jefferson Lab.