This entry in the Encyclopedia of Complexity and Systems Science, Springer present a summary of some of the concepts and calculational tools that have been developed in attempts to apply statistical physics approaches to seismology. We summarize the leading theoretical physical models of the space-time organization of earthquakes. We present a general discussion and several examples of the new metrics proposed by statistical physicists, underlining their strengths and weaknesses. The entry concludes by briefly outlining future directions. The presentation is organized as follows. I Glossary II Definition and Importance of the Subject III Introduction IV Concepts and Calculational Tools IV.1 Renormalization, Scaling and the Role of Small Earthquakes in Models of Triggered Seismicity IV.2 Universality IV.3 Intermittent Periodicity and Chaos IV.4 Turbulence IV.5 Self-Organized Criticality V Competing mechanisms and models V.1 Roots of complexity in seismicity: dynamics or heterogeneity? V.2 Critical earthquakes V.3 Spinodal decomposition V.4 Dynamics, stress interaction and thermal fluctuation effects VI Empirical studies of seismicity inspired by statistical physics VI.1 Early successes and latter subsequent challenges VI.2 Entropy method for the distribution of time intervals between mainshocks VI.3 Scaling of the PDF of Waiting Times VI.4 Scaling of the PDF of Distances Between Subsequent Earthquakes VI.5 The Network Approach VII Future Directions
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