Sometime between 2006 and 2012, the broad Hβ emission line of Mrk 590, once classified as a bona-fide Seyfert 1 galaxy, has completely disappeared! The optical-UV continuum emission has decreased to the point where it can be fully accounted for by stellar population models of the host galaxy. As such, Mrk 590 would now be classified as a Seyfert 1.9 or 2 galaxy, which goes against the prevailing scheme of AGN classification and unification where the presence of broad emission lines depends only on source orientation. Similar decreases in X-ray and radio continuum fluxes show that the central engine of Mrk 590 may be turning off or transitioning into a radiatively inefficient mode of accretion. We discuss the origin of the compact, unresolved radio emission in Mrk 590 and the physics of its variability in relation to the variability observed at other wavelengths, based on archival radio data and new VLBI observations. We also present recent ALMA observations of the CO(3-2) spectral line and sub-mm continuum emission; these provide the strongest limits to date on the molecular gas mass in the central ~100 pc, plus reveal the gas distribution and kinematics in the central kpc, to determine if this intriguing AGN is indeed running out of fuel.