Voids represent a unique environment for the study of galaxy evolution, as the lower density environment is expected to result in shorter merger histories and slower evolution of galaxies. This provides an ideal opportunity to test theories of galaxy formation and evolution. Imaging of the neutral hydrogen, central in both driving and regulating star formation, directly traces the gas reservoir and can reveal interactions and signs of cold gas accretion. For a new Void Galaxy Survey (VGS), we have carefully selected a sample of 59 galaxies that reside in the deepest underdensities of geometrically identified voids within the SDSS at distances of ~100 Mpc, and pursued deep UV, optical, Halpha, IR, and HI imaging to study in detail the morphology and kinematics of both the stellar and gaseous components. This sample allows us to not only examine the global statistical properties of void galaxies, but also to explore the details of the dynamical properties. We present an overview of the VGS, and highlight key results on the HI content and individually interesting systems. In general, we find that the void galaxies are gas rich, low luminosity, blue disk galaxies, with optical and HI properties that are not unusual for their luminosity and morphology. We see evidence of both ongoing assembly, through the gas dynamics between interacting systems, and significant gas accretion, seen in extended gas disks and kinematic misalignments. The VGS establishes a local reference sample to be used in future HI surveys (CHILES, DINGO, LADUMA) that will directly observe the HI evolution of void galaxies over cosmic time.