Countries around the world suffer the dramatic impact of earthquakes and other natural hazards reflected in casualties, infrastructure damage, service interruptions, and recovery costs. Although disaster exposure consciousness of electric power systems has increased in recent years, mitigation and adaptation actions, such as reserve scheduling and infrastructure investments, are usually performed without quantitative tools to account for the underlying stochasticity of these events. This article first discusses why an integrated assessment, which incorporates sources of uncertainty (risk) and manages the time-dependency of the recovery process (resilience), should be used to assess the impact of seismic events on electric power systems. Thereafter, a probabilistic methodology that considers the hazard, vulnerability, operation, and recovery of the system is presented. As a case study, the probabilistic seismic resilience of the electric power system of Northern Chile is assessed using different risk measures, including expected annual loss, value at risk, and conditional value-at-risk. Finally, a novel criticality assessment based on these metrics is developed to demonstrate that, for certain networks such as the study case, retrofit of selective components can notably improve the resilience of the complete system to seismic events. For example, if one specific component from the 152 components of the study system is assumed invulnerable, expected annual interruption costs decrease by 8%.