The risk of intentional attacks from terrorism is fundamentally different from other types of hazards, like accidents or acts of nature, as intelligent and adaptable adversaries will change offensive strategies and adapt their tactics to bypass or circumvent defenses. Approaches to risk assessment and management that may work well in other contexts (e.g., protecting against accidents or acts of nature) can fail to correctly anticipate and quantify the risks from intelligent, adaptive adversaries. Therefore, a more effective approach is needed; methods for guiding resource allocations to defend against terrorism must explicitly take into account the intelligent and adaptive nature of the threat. The incomplete understanding of the motivating factors and payoffs to terrorists further complicates the analysis of terrorist threats, and these factors must be inferred in a data-poor environment and where direct access to terrorists is seldom possible. Our research team uses extensions of probabilistic risk analysis of engineered systems, game theory, and expert elicitation of risks and uncertainties to address this problem in all three contexts - terrorism, natural disasters, and man-made accidents.