 Given the grand scope of cosmology, one might expect that many questions must remain unresolved. Basic features of the SM impose two fundamental limits to the ambitions of cosmological theorizing. First, the finitude of the speed of light ensures that we have a limited observational window on the universe due to existence of the visual horizon, representing the most distant matter from which we can receive and information by electromagnetic radiation, and the particle horizon, representing the most distant matter with which we can have had any causal interaction (matter up to that distance can influence what we see at the visual horizon). Recent work has precisely characterized what can be established via idealized astronomical observations, regarding spacetime geometry within, or outside, our past light cone (the observationally accessible region). Second, in addition to enormous extrapolations of well-tested physics in the SM, cosmologists have explored speculative ideas in physics that can only be tested through their implications for cosmology; the energies involved are too high to be tested by any accelerator on Earth. Ellis (2007) has characterized these speculative aspects of cosmology as falling on the far side of a “physics horizon”. We will briefly discuss how this second type of horizon poses limits for cosmological theorizing. In both cases, the type of underdetermination that arises differs from that discussed in the philosophical literature.