Fast and accurate unveiling of power-line outages is of paramount importance not only for preventing faults that may lead to blackouts but also for routine monitoring and control tasks of the smart grid. This chapter presents a sparse overcomplete model to represent the effects of (potentially multiple) power line outages on synchronized bus voltage angle measurements. Based on this model, efficient compressive sensing algorithms can be adopted to identify outaged lines at linear complexity of the total number of lines. Furthermore, the effects of uncertainty in synchronized measurements will be analyzed, along with the optimal placement of measurement units.