The interactions between young planets and the circumstellar disks in which they form create gaps and asymmetries that encode planet mass and orbital radius. The ngVLA will provide a unique combination of angular resolution and sensitivity at wavelengths of 3 to 10 millimeters to reveal these structures in the terrestrial planet formation zones of disks in nearby star-forming regions. Detailed simulations of planet-disk interactions show that ngVLA images of dust continuum emission can readily detect the rings and gaps produced by a forming Earth-mass planet around a Sun-like star (or a Mars-mass planet around a 0.1 Solar mass M dwarf) with orbital radii of 1 to 3 au. For more massive planets, the ngVLA will also detect the azimuthal structures predicted to form in disks of low viscosity. Given the short orbital timescales at these radii, proper motions of these structures can be followed by observations separated by days, weeks, and months, and these multi-epoch observations will yield “movies” that provide new ways to probe the physics of planet-disk interactions. Observations of large samples will constrain the planet initial mass function and provide a framework to understand the origins of exoplanet demographics. The Next Generation Very Large Array is a design and development project of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc.