This paper describes results from the analysis of two approaches to blackout risk analysis in electric power systems. In the first analysis, we compare two topological (graph-theoretic) methods for finding vulnerable locations in a power grid, to a simple model of cascading outage. This comparison indicates that topological models can lead to misleading conclusions about vulnerability. In the second analysis, we describe preliminary results indicating that both a simple dynamic power system model and frequency data from the August 10, 1996 disturbance in North America show evidence of critical slowing down as the system approaches a failure point. In both examples, autocorrelation in the time- domain signals (frequency and phase angle), significantly increases before reaching the critical point. These results indicate that critical slowing down could be a useful indicator of increased blackout risk.