Global anomalies in gauge theories are detected by the exponentiated eta-invariant, which becomes a cobordism invariant when perturbative anomalies vanish. After giving a gentle introduction to these concepts, I will analyse global anomalies in four distinct (but equally valid) versions of the Standard Model by computing appropriate bordism groups. In two cases we find no global anomalies beyond the famous Witten anomaly associated with electroweak SU(2) symmetry, while in the other two cases there can be no global anomalies at all. This is due to an interplay between local and global anomalies in "closely related" gauge theories. If there is time, I will discuss a more subtle version of this anomaly interplay occurring in a U(2) gauge theory defined without a spin structure, and/or global anomalies in BSM theories.