New and forthcoming instruments are poised to detect the observational signatures of the first metal-free, Population III (Pop III), stars. For instance, the James Webb Space Telescope may detect Pop III pair-instability supernovae and large ground-based telescopes such as GMT, TMT, and ELT will take spectra of many stars in our Galaxy to perform stellar archaeology. A detailed understanding of Pop III stars is crucial for interpreting the earliest stages of galaxy evolution. Additionally, because Pop III stars are predicted to form in extremely low-mass dark matter halos, they provide an opportunity to constrain the particle nature of dark matter (models such as warm or “fuzzy” dark matter suppress small-scale structure). I will discuss my group’s recent hydrodynamical cosmological simulations of the first stars that predict the minimum halo mass required for star formation as a function of environmental properties (e.g., the so-called baryon-dark matter streaming velocity and UV background radiation). I will then describe how these results are applied to our computationally efficient semi-analytic models to make large-scale predictions such as the global star formation history of Pop III stars. Finally, I will present numerical simulations of the formation of the first stars in a fuzzy dark matter (FDM) cosmology (e.g., composed of ultra-light axions). FDM is an alternative dark matter candidate motivated by small-scale discrepancies with the standard CDM model. We performed numerical simulations of the first stars in an FDM cosmology accurately following the primordial chemistry and gas cooling until runaway collapse. We find that FDM results in “pancakes” of Pop III stars, much different than the star clusters formed in quasi-spherical halos in LCDM, that are potentially observable with the James Webb Space Telescope.