Abstract | We discuss the current state-of-the-art on the assessment of systems (structures and lifelines) subjected to seismic loading. Severe earthquakes are random events that may have a devastating outcome. Therefore, the treatment of seismic loading and its effects has many layers due to the random nature of the problem and also its consequences. We attempt to provide a wide approach to the problem, referencing the major contributions in the field and discussing the most suitable methods for tackling the challenges involved. Our study extends from modeling seismic hazard to the modeling and analysis of structures and lifelines. Emphasis is given to probabilistic performance estimation frameworks and the rational treatment of uncertainty, a major element of contemporary earthquake engineering.