This set of slides was presented at the CNLS Smart Grid Seminar Series at Los Alamos National Lab in July 2009. It describes ongoing work with new methodologies for two classes of problems: (1) vulnerability analysis of large-scale transmission systems, and (2) algorithms for throughput maximization in transmission systems. Vulnerability analysis, in particular the so-called "N-k" problem and derivatives, are well-known. The results are presented with a mixed-integer programming formulation that addresses a standard version of the problem. Then, the results with an indirect approach are presented that proves vastly more scalable and informative while at the same time being able to address a more realistic version of the problem, including 'noise' and model uncertainty.