Humans derive benefits from ecosystems in multiple ways. As ecosystems move and are disrupted by the changing climate, these benefits will change or disappear. In this dissertation, I explore what are the consequences to society of those changes on market and non-market components of human well-being provided by ecosystems throughout the globe. I use an integrated approach to model the interactions between climate, economics and ecosystems, allowing to estimate climate policy-relevant metrics such as the social cost of carbon. The Introduction of this dissertation is a review of the state of the literature on natural capital and the social cost of carbon highlighting key research areas to advance this field. The first chapter presents GreenDICE, an Integrated Assessment Model (IAM) that extends the standard Dynamic Integrated Climate-Economy (DICE) model to account for natural capital and its role in providing use and non-use benefits to people. The second chapter extends GreenDICE to account for process-based ecosystem dynamics and allow for geographical heterogeneity among countries in relation to their dependence on natural capital for the creation of market and out-of-market goods and services. Finally, the third chapter turns to the empirical question of whether there is evidence of persistent effects of temperature on gross domestic product (GDP), such as the ones we would expect to see in an economy that relies on productive assets that in turn are damaged by climate change, as in the case of natural capital in GreenDICE. Overall, the results show that explicitly including ecosystems as a form of capital assets in IAMs increases by an order of magnitude the social cost of carbon. Moreover, these impacts will not be equally distributed across the world. The market economies of low-income countries will be the most affected by climate change-disturbed ecosystems, posing an additional mechanism for intensifying inequality. The empirical evidence shows that it is likely that some country-level economies might have already experienced persistent temperature effects on GDP, supporting modeling approaches as GreenDICE that include temperature impacts on the economic productive base.