An enormous volume of security-relevant information is present on the Web, for instance in the content produced each day by millions of bloggers worldwide, but discovering and making sense of these data is very challenging. This paper considers the problem of exploring and analyzing the Web to realize three fundamental objectives: 1.) security relevant information discovery; 2.) target situational awareness, typically by making (near) real-time inferences concerning events and activities from available observations; and 3.) predictive analysis, to include providing early warning for crises and forming predictions regarding likely outcomes of emerging issues and contemplated interventions. The proposed approach involves collecting and integrating three types of Web data, textual, relational, and temporal, to perform assessments and generate insights that would be difficult or impossible to obtain using standard methods. We demonstrate the efficacy of the framework by summarizing a number of successful real-world deployments of the methodology.