This thesis investigates how the theoretical predictions of traditional economic models change when the assumption of Bayesian decision making is relaxed. Bayesian decision theory assumes that decision makers are able to perfectly describe their state space and assign a single prior to every possible event. The theory of unawareness relaxes the first assumption by allowing decision makers to be aware of some contingencies and unaware of others. The theory of ambiguity relaxes the second assumption and allows decision makers to prefer known risks over unknown risks. The first chapter of this thesis analyzes the effect of ambiguity on bilateral trade in the presence of private information. It demonstrates that in an environment with adverse selection as in Akerlof's (1970) market for lemons, screening the informed party hedges against ambiguity. It further shows that the presence of ambiguity can be both beneficial or harmful for trade. If the adverse selection problem is sufficiently severe, more ambiguity surprisingly leads to more trade and thereby increase surplus. Using these results, a financial market application demonstrates that ambiguity may help to explain why some assets are optimally traded over-the-counter rather than on traditional exchanges, and suggests that opacity may be essential to sustain such trade. The second chapter of this thesis introduces asymmetric awareness into a classical principal-agent model with moral hazard, and shows how unawareness can give rise to incomplete contracts. The paper investigates the optimal contract between a fully aware principal and an unaware agent, where the principal can enlarge the agent's awareness strategically. When proposing the contract, the principal faces a tradeoff between participation and incentives: leaving the agent unaware allows the principal to exploit the agent's incomplete understanding of the world, relaxing the participation constraint, while making the agent aware enables the principal to use the revealed contingencies as signals about the agent's action choice, relaxing the incentive constraint. The optimal contract reveals contingencies that have low probability but are highly informative about the agent's effort.