Dark matter is by nature extremely difficult to detect. The only force we are certain it interacts with is gravity, making gravitational studies a key tool for investigating different models. In this thesis, a Jeans kinematic analysis and gravitational waves are used to study the viability of dark matter models that are alternatives or complements to Cold Dark Matter. I study whether ultralight bosonic dark matter is consistent with the gravitational potential extracted from stellar kinematics. The posterior likelihood is multimodal. Particle masses of order $m\sim10^{-22}$ eV require halos of mass in excess of $\sim10^{10}M_\odot$, while particle mass of order $m\geq 10^{-20}$ eV are favored by halos of mass $\sim[10^8-10^9]M_\odot$, with a similar behavior to cold dark matter. Regardless of particle mass, the lower halo masses are allowed if stellar dynamics are influenced by the presence of a central black hole of mass at most $\sim10^{-2}$ the host halo mass. There is no preference for models that contain a black hole over models that do not contain a black hole. I conclude that either the fuzzy dark matter particle mass must be $m\geq 10^{-20}$ eV, or the Milky Way dwarfs must be unusually heavy given the expected hierarchical assembly of the Milky Way, or the Milky Way dwarfs must contain a central black hole. I find no evidence for either of the last two possibilities and consider them unlikely. I also study Primordial Black Holes as a possible explanation for the $2.6 M_\odot$ object in the LIGO/Virgo GW190814 merger observed in gravitational waves. Primordial black holes could make up a fraction of the universe's dark matter; this object is a candidate as it would be either the heaviest neutron star or lightest black hole observed to date. I find that a primordial black hole explanation to GW190814 is unlikely as it is limited by the formation rate of the primary stellar progenitor and the time available for a pair of primordial- and stellar-origin black hole binaries to form and merge within a Hubble time.
