The unprecedented imaging capabilities offered by the Atacama Large Millimeter Array (ALMA) and the Karl Jansky Very Large Array (JVLA) are transforming our understanding of planet formation. During my talk, I will review the most recent millimeter-wave observations of nearby young circumstellar disks that probe the spatial distribution and the physical properties of the circumstellar dust and gas, and reveal planetary systems in the act of forming. I will discuss these observations in the framework of the demographics of the known exoplanetary systems and of the current planet formation models. Finally, I will briefly present two newborn initiatives aimed to build next generation interferometers capable of mapping nearby proto-planetary disks at sub-AU resolution.