Every day, individuals around the world retrieve, share, and exchange information on the Internet. We interact online to share personal information, find answers to questions, make financial transactions, play social games, and maintain professional and personal relationships. Sometimes our online interactions take place between two or more humans. In other cases, we rely on computers to manage information on our behalf. In each scenario, risk and uncertainty are essential for determining possible actions and outcomes. This essay highlights common deficiencies in our understanding of key concepts such as trust, trustworthiness, cooperation, and assurance in online environments. Empirical evidence from experimental work in computer-mediated environments underscores the promises and perils of overreliance on security and assurance structures as replacements for interpersonal trust. These conceptual distinctions are critical because the future shape of the Internet will depend on whether we build assurance structures to limit and control ambiguity or allow trust to emerge in the presence of risk and uncertainty.