Predicting singular/extremal phenomena exceeding certain spatial, temporal, or energetic scales remains as a main scientific and practical challenge. The question is: does modern geophysics - based on recent progress in theories of complex systems and nonlinear dynamics - provide useful scientific insights to mechanisms underlying disastrous extreme events? The question is of primary importance, because providing more reliable disaster prediction methodologies is closely tied with scientific understanding of the hazardous process. From the point of view of dynamics, hazardous natural phenomena such as earthquakes, floods, or landslides are recognized as complex and high-dimensional processes. For such randomlike processes with no (or weak) inherent determinism, there are major, perhaps fundamental, difficulties in creating a comprehensiv physical/mathematical theory to describe and predict their evolution in spatial, temporal or energetic domains. At the same time, the weakness of deterministic relations in high dimensional processes does not imply an absence of order in governing rules. This is why for complex natural systems very large deviations from the mean (catastrophic extreme events) are not negligible and originate from system's inherent rules, not from chance. The most important features of complex systems are their ability to self-organize and the fractal distributions. For commonly limited natural scales it reveals itself in the form of memory or long-range dependence. According to the present understanding almost all important natural hazards are associated with such memory, scale invariant, close-to-critical state models, e.g. landslides with the sand-pile model, earthquakes with the slider-block model, and forest fires with the forest-fire model. In spite of present difficulties related to the correct dynamical analysis of complex systems, it is accepted that predictability of natural disasters can be considered as a well-posed task. Thus, developing dynamical methods together with quantitative models needed to evaluate probabilistic hazard assessment is within our reach. This will require a combined effort of earth scientists, physicists, statisticians, and practitioners. In this chapter we present a short review of dynamics and predictability of complex processes as well as some results of seismic hazard assessment in Georgia.