Abstract: The sensitivity and resolution of the Atacama Large Millimeter/Submillimeter Array (ALMA) have enabled detailed study of protoplanetary disk structure and kinematics. By forward modeling the interferometric measurement sets from ALMA we can infer the disk velocity field, empirically measure stellar masses, and unlock pre-main sequence system architectures. Our observations of protoplanetary disks in binary star systems have provided context needed to understand the circumbinary planet population as probed by the Kepler Mission, an effort that has historically been hampered by the fact that occurrence rate is degenerate with assumptions about the typical misalignment between the binary and planetary orbital planes. Our survey of 20 spatially-resolved circumbinary protoplanetary and debris disks includes several spectroscopic binaries (P < 40 days) whose disks we have resolved with ALMA for the first time and are the only protoplanetary systems comparable in scale to the Kepler circumbinary planet hosts. We use a hierarchical Bayesian model to infer that the mutual inclination distribution of circumbinary disks around spectroscopic binaries is intrinsically low, suggesting that Kepler did not miss a large population of mis-aligned circumbinary planets, and that circumbinary planets occur at a similar rate as those around single stars. Throughout my talk, I will discuss several of the data driven and forward modeling techniques that we developed to probe the planet forming environment with exquisite precision, including template-free spectroscopic disentangling with Gaussian processes and regularized maximum likelihood image reconstruction. Techniques like these will be indispensable for sensing the velocity field with sufficient precision to infer protoplanet properties from their kinematic perturbations.