Integrated Assessment Models (IAMs) of the climate and economy aim to analyze the impact and efficacy of policies that aim to control climate change, such as carbon taxes and subsidies. A major characteristic of IAMs is that their geophysical sector determines the mean surface temperature increase over the preindustrial level, which in turn determines the damage function. Most of the existing IAMs are perfect-foresight forward-looking models, assuming that we know all of the future information. However, there are significant uncertainties in the climate and economic system, including parameter uncertainty, model uncertainty, climate tipping risks, economic risks, and ambiguity. For example, climate damages are uncertain: some researchers assume that climate damages are proportional to instantaneous output, while others assume that climate damages have a more persistent impact on economic growth. Climate tipping risks represent (nearly) irreversible climate events that may lead to significant changes in the climate system, such as the Greenland ice sheet collapse, while the conditions, probability of tipping, duration, and associated damage are also uncertain. Technological progress in carbon capture and storage, adaptation, renewable energy, and energy efficiency are uncertain too. In the face of these uncertainties, policymakers have to provide a decision that considers important factors such as risk aversion, inequality aversion, and sustainability of the economy and ecosystem. Solving this problem may require richer and more realistic models than standard IAMs, and advanced computational methods. The recent literature has shown that these uncertainties can be incorporated into IAMs and may change optimal climate policies significantly.