  We review the present status of our research and understanding regarding the
dynamics and the statistical properties of earthquakes, mainly from a
statistical physical viewpoint. Emphasis is put both on the physics of friction
and fracture, which provides a "microscopic" basis of our understanding of an
earthquake instability, and on the statistical physical modelling of
earthquakes, which provides "macroscopic" aspects of such phenomena. Recent
numerical results on several representative models are reviewed, with attention
to both their "critical" and "characteristic" properties. We highlight some of
relevant notions and related issues, including the origin of power-laws often
observed in statistical properties of earthquakes, apparently contrasting
features of characteristic earthquakes or asperities, the nature of precursory
phenomena and nucleation processes, the origin of slow earthquakes, etc.
