  We examine simple models with an inert scalar and vector-like leptons that
can explain the recent $g_{\mu}-2$ measurement reported at FNAL. Prompted by
this exciting result, we explore the viability of a simple interpretation and
determine the required parameters. We also embed these models within a 3-3-1
gauge extension of the Standard Model (SM), showing that the $g_{\mu}-2$
anomaly can be accommodated in agreement with current data. We also show how
our theory can be tested at high-energy colliders such as HL-LHC and FCC-hh.
