I review the motivation for extending the SM gauge group by an additional U(1) gauge symmetry, with an emphasis on anomaly-free vs. anomalous choices. Besides the simple but rich Z’ physics from such extensions, the anomalous models also feature new fermions with electroweak couplings and a new Higgs boson at a minimum. A critically important prediction in these models is the anomaly-mediated exotic decay of Z to Z’ and a photon if m_Z’ < m_Z, where the current BR constraint in the dilepton + gamma or dijet + gamma final state comes from the L3 experiment and is at the 10^-4 level. Additional collider signals include BSM Higgstrahlung from the Z’ boson and Z’-mediated VBF production of the BSM Higgs boson, leading to multijet and diphoton resonances when the Z’ mediates a quark-universal gauge symmetry.