The Pacific Northwest National Laboratory (PNNL) consistently delivers high-quality methods and novel applications to address critical scientific challenges in national security and energy resiliency. Through the application of core competences in mathematics, statistics, operations research, data analytics, and software engineering, PNNL researchers help decision makers make better informed choices in mission-critical domains. This presentation will overview capabilities within our Computing and Analytics Division and the Applied Statistics and Computational Modeling Group along with the diverse nature of some of our research projects. The presentation will then focus on some of the mathematics behind our risk-based quantification and resource allocation techniques. Finally, opportunities available to students and graduates will also be discussed.