Despite decades of research on the science and potential impacts of climate change, considerable disagreement remains over how to balance the upfront costs of reducing greenhouse gas emissions with the benefits of avoiding future negative impacts. This disagreement persists, in part, because deep uncertainties in the climate system limit our understanding of how temperature and sea level will evolve over the coming centuries. The global nature and long timescales of climate change provide an additional challenge, as climate policy analysis requires difficult ethical judgments on how to value the well-being of individuals at different income levels and across generations. In this dissertation, I address these issues by using integrated assessment models (IAMs) to analyze how distributional equity concerns and previously neglected climate uncertainties affect climate policy design. In the first part, I calculate the optimal carbon dioxide mitigation policy when society accounts for the trade-off between mitigation costs, climate damages, and the climate and localized health consequences of changes in air pollutant co-emissions. The presence of health “co-benefits” leads to increased mitigation levels that may be consistent with a 2 °C target, but the magnitude of this effect crucially depends on independent air quality policies and the value society assigns to improvements in human health. In the second part, I use a Bayesian calibration framework and an ensemble of IAMs to quantify how parametric climate uncertainties affect the social cost of methane (SC-CH4). Despite accounting for the recent 25% upward revision to methane radiative forcing, the constrained models produce a mean SC-CH4 estimate 23% lower than the value recently used by the U.S. federal government. I also provide the first probabilistic equity-weighted SC-CH4 estimates and find that the U.S. value is more than an order of magnitude higher than sub-Saharan Africa’s. The third part of my dissertation focuses on low-probability, high-impact upper tail estimates of the social cost of carbon (SCC). In this analysis, I first show that the simple climate models from the IAMs used to calculate official U.S. SCC estimates do not pass relatively simple out-of-sample hindcast tests and exhibit impulse response behaviors that are inconsistent with current scientific understanding. I then couple the non-climate components of each IAM to a reduced complexity Earth system model and quantify how different treatments of parametric uncertainties affect 95th percentile SCC estimates. While failing to account for interactions between the uncertain parameters increases the 95th percentile SCC by more than 20%, following the official U.S. SCC climate uncertainty framework nearly doubles it.