This chapter describes methods to detect and identify power system transmission line outages in near real time. These methods exploit statistical properties of the small random fluctuations in electricity generation as well as energy demand to which a power system is subject to as time evolves. To detect and identify transmission line outages, a linearized incremental small-signal power system model is used in conjunction with high-speed synchronized voltage phase angle measurements obtained from phasor measurement units. By monitoring the statistical properties of voltage phase angle time-series, line outages are detected and identified using techniques borrowed from the theory of quickest change detection. Several case studies are considered for the cases of detecting and identifying single- and double-line outages in an accurate and timely fashion.