Cascading failures present severe threats to power grid security, and thus vulnerability assessment of power grids is of significant importance. Focusing on analytic methods, this paper reviews the state of the art of vulnerability assessment methods in the context of cascading failures. These methods are based on steady-state power grid modeling or high-level probabilistic modeling. The impact of emerging technologies including phasor technology, high-performance computing techniques, and visualization techniques on the vulnerability assessment of cascading failures is then addressed, and future research directions are presented.