  We revisit various topological issues concerning four-dimensional ungauged
and gauged Wess-Zumino-Witten (WZW) terms for $SU$ and $SO$ quantum
chromodynamics (QCD), from the modern bordism point of view. We explain, for
example, why the definition of the $4d$ WZW terms requires the spin structure.
We also discuss how the mixed anomaly involving the 1-form symmetry of $SO$ QCD
is reproduced in the low-energy sigma model.
