Advances in observational abilities from the likes of the James Web Space Telescope, the Rubin Observatory, and the LIGO‐Virgo‐KAGRA collaboration anticipate observations of the cosmos at smaller scales than ever before. At the same time, the dearth of non‐gravitational dark matter detections and ongoing small‐scale tensions, like the core/cusp problem, incentivize the search for new dark matter models that may offer solutions to these tensions without requiring strong Standard Model interactions. Dissipative dark matter models may provide an answer to the general dark matter problem and some of the small‐scale tensions, with the further intriguing possibility that some dark matter halos could directly collapse into dark compact objects. My talk focuses on the contributions I have made to using current and future observables to constrain dissipative dark matter as well as simulating the behavior of one of these models, atomic dark matter, in both collapsing dark matter halos and in the form of dark white dwarfs. I describe the necessity for a new constraints paradigm, based on constraining the dark cooling function across different cosmic scales, as well as showing the current status of said constraint. I include a method for re‐scaling Standard Model chemical rates to construct the equivalent rate in the atomic dark matter model, and demonstrate its use with the construction of a minimal dark reaction network and the development of dark molecular cooling rates for use in dark astrochemistry. Since many dark matter simulations now involve large n‐body codes with external astrochemistry libraries, I describe the DarkKROME software package that I developed which can solve dark astrochemical problems using the aforementioned dark reactions and thermal processes. Finally, I discuss a possible type of exotic compact object, the dark white dwarf, which has unique physical properties and could be observed by gravitational wave observatories in the near future.