Abstract: It is now known that a significant fraction of the Milky Way ISM resides in a so-called "dark" phase, usually defined as a mixture of cold, optically thick HI and diffuse molecular hydrogen with densities that are insufficient to form and shield CO. I will present a brief overview of the so-called "Dark ISM" -- where it resides, how much there is, and its characteristic properties. I will then focus on two aspects of structure in the dark gas: (1) AU-scale structures in the cold atomic medium, including their possible implications in measuring the fraction of cold/opaque HI, and (2) underlying structure in CO-dark molecular gas that can give rise to very broad, very weak molecular spectral features in OH and HCO+. I will introduce two ongoing observational experiments that may further constrain both of these phenomena.