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This book assembles, identifies and highlights the most recent developments in Rehabilitation and retrofitting of historical and heritage structures. This is an issue of paramount importance in countries with great built cultural heritage that also suffer from high seismicity, such as the countries of the eastern Mediterranean basin. Heritage structures range from traditional residential constructions to monumental structures, ancient temples, towers, castles, etc. It is generally recognized that these structures present particular difficulties in seismic response calculation through computer simulation due to the complexity of the structural system which is, generally, inhomogeneous, with several contact problems, gaps/joints, nonlinearities and brittleness in material constituents. This book contains selected papers from the ECCOMAS Thematic Conferences on Computational Methods in Structural Dynamics & Earthquake Engineering (COMPDYN) that were held in Corfu, Greece in 2011 and Kos, Greece in 2013. The Conferences brought together the scientific communities of Computational Mechanics, Structural Dynamics and Earthquake Engineering in an effort to facilitate the exchange of ideas in topics of mutual interest and to serve as a platform for establishing links between research groups with complementary activities.