The Fermi constant G_F is extremely well measured through the muon lifetime, defining one of the key fundamental parameters in the standard model (SM). Therefore, to search for physics beyond the SM (BSM) via G_F, the constraining power is determined by the precision of the second-best independent determination of G_F. The best alternative extractions of GF proceed either via the global electroweak (EW) fit or from superallowed β decays in combination with the Cabibbo angle measured in kaon, τ, or D decays. Both variants display some tension with GF from muon decay, albeit in opposite directions, reflecting the known tensions within the EW fit and hints for the apparent violation of Cabibbo-Kobayashi-Maskawa unitarity, respectively. We investigate how BSM physics could bring the three determinations of G_Finto agreement using SM effective field theory and comment on future perspectives.