Cold gas plays a central role in feeding and regulating star formation and growth of supermassive black holes (SMBH) in galaxy nuclei. Particularly powerful activity occurs when interactions of gas-rich galaxies funnel large amounts of gas and dust into nuclei of luminous and ultra luminous infrared galaxies (LIRGs/ULIRGs). These dusty objects are of key importance to galaxy mass assembly over cosmic time and studying them is fundamental to our understanding of galaxy evolution. Recent studies reveal that some (U)LIRGS have very deeply embedded galaxy nuclei – hiding an unknown luminosity source: the Compact Obscured Nuclei (CONs). Our ALMA observations show that CONs are common in U/LIRGs – but what is lurking behind the masses of dust? A hidden phase of efficient black hole accretion – and/or an extremely compact burst of star formation? We need to go to long wavelengths to probe behind the veil of dust: mm/submm wavelengths with ALMA, cm wavelengths with VLA and the future ngVLA or SKA. We can also go to the far-infrared using space-based telescopes. I will present some initial ALMA high-resolution studies of the CON-LIRG IC860, the ex-CON lenticular NGC1377 – and demonstrate the power of high resolution and sensitivity in probing the enshrouded nuclei and their feedback. I will also show the first results from the ALMA CONquest survey and also how the VLA can reach behind the curtain of dust to undertake new studies of heretofore hidden, rapid evolutionary phases of galaxy nuclei. Do CONs represent a new, unknown evolutionary phase of nuclear growth?