Most economic environments are characterized by uncertainty. Economic agents thus have to make decisions, the consequences of which cannot be known ex ante. Decision theory studies this process of decision making and tries to identify how the description of uncertainty influences beliefs, and through them, the evaluation of uncertain acts. This, in turn, allows us to make testable predictions about behavior and study the implications of uncertainty on economic outcomes. Ambiguity, i.e., the fact that decision makers face uncertainty about the probability distribution governing the outcomes, has been found to have a significant impact on human behavior. In this project, we study decision making under ambiguity when information is provided in the form of data. While data carry objective information about the stochastic process of outcomes, this information might be insufficient to uniquely identify the probability distribution of outcomes. We examine the relation between objective information provided by data and decision maker's beliefs about uncertain outcomes. We analyze how the type and frequency of observations combine with the subjective characteristics of the decision maker to determine his beliefs and, in turn his behavior in view of this ambiguity. An important question in decision theory concerns the value of additional information. While it is known that for Bayesian agents, additional information is always beneficial, this need not be the case for agents who are not neutral towards ambiguity. We thus study the value of acquiring additional data as a function of the characteristics of the data and the individual characteristics of the agent, such as his degrees of optimism and pessimism. In the second part of the project, we apply the framework developed above to different economic problems characterized by ambiguity. We study the behavior of ambiguity-averse investors in a financial market and identify the long-run impact of ambiguity and ambiguity-aversion on equilibrium prices and allocations. We analyze the process of technology adoption as an important mechanism of adaptation to climate change. In particular, we examine the impact of optimism and pessimism on learning and on optimal technology choice. We also evaluate different policies designed to stimulate early adoption. Finally, we study the decision of market participation, when markets provide different type and different quantity of information. We show that agents self-select into markets depending on their preferences for information, which, in turn determines the market structure in a given economy. We use these insights to derive implications for the optimal design and regulation of markets.