An overview is presented of studies about the application of the life-cycle optimization approach to the establishment of seismic design criteria and maintenance policies, taking into account the influence of damage accumulation. For these purposes, seismic hazard is described by probabilistic models of the stochastic process of the occurrence of earthquake ground motions of different intensities at a site; the implications of adopting Poisson, renewal and Markov process models are examined. Mechanical properties of the structural systems considered are taken as uncertain. They are assumed to remain constant between repair and maintenance actions, but may be modified by the latter. Because the process of damage accumulation depends on the mechanical properties that determine the dynamic response of the system to ground motions of different intensities, and these in turn depend on both initial damage and that accumulated as a result of previous seismic events, the former process has to be represented by a Markov model. Several groups of uncertainties are considered: a) those associated with the times of occurrence, intensities and detailed characteristics of the seismic events, b) those related to the actual values of mechanical properties of the structural system, as compared with those assumed during the process of structural design, and c) epistemic uncertainties representing our imperfect knowledge about the models used in the analysis, including those used to describe seismic hazard as well as those related to the models used to represent the cyclic behaviour of the structural system when responding to earthquake ground motions of different intensities. Uncertainties in the first two groups are random variables that can vary either from event to event or between repair and maintenance actions, while the probabilistic models of those in the third group can be updated on the basis of learning accumulated from observations about both the seismic process and the dynamic response and performance of the system. The determination of optimum design criteria and target performance levels is based on the maximization of an objective function represented by the sum of the present values of expected costs. This function is calculated multiplying the nominal values of the expected consequences of future events by discount functions that decrease with increasing values of the time to the occurrence of those events. For those cases where seismic activity at the site of interest is represented by renewal or Markov process models, seismic hazard increases systematically with time, and so does seismic risk for a system with constant properties. This means that, as time goes, a decision that was optimum at the time when it was made may lead to unacceptable risk levels for future generations. Therefore, possible future actions to cope with this problem have to be examined during the process of the initial decision. Several examples are presented to illustrate the applications of the above concepts to specific cases of interest for engineering practice. For systems with energy dissipating devices, the decision process may include variables and concepts such as the selection of times or threshold damage levels for repair of the main system or for replacement of the energy dissipating devices. They also include the adoption of design criteria oriented to concentrating structural damage at locations or elements where actions of local repair or replacement are simpler and less expensive.