At present, there are two major concepts, adopted for description of seismic process. The simplest of them, namely, Poissonian model, now dominant, is a basis of widely accepted modern methods of Probabilistic Seismic Hazard Assessment. According to this model, the seismic events are independent of each other, i.e. the long-term correlations are absent in seismic process, which means that it can be described in terms of classic Boltzman-Gibbs (B-G) thermodynamics. Last decades, application of modern methods of complexity analysis revealed undeniable arguments in favour of existence of long-term correlations in temporal, spatial and energy distributions of seismic events, leading to power-law distributions in all three domains. As a result, nonlinear (hidden) structures were discovered in seismic data sets and their characteristics were calculated: it turned out that they vary with time, which is in contradiction with memoryless purely Poissonian approach. There is a hope that the analysis of temporal variations of complexity (seismic) measures offer a challenge of more well founded forecasting strong earthquakes.