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Mathematical models and methods are required for diverse studies in Geosciences and simultaneously, new problems are posing new needs where Mathematics is needed. At the initiative of American and Canadian research mathematical institutes and societies, year 2013 was declared a thematic year in Mathematics and the Planet Earth, under the patronage of UNESCO. To mark the MPE2013, and highlight the two-way street between Mathematics and Earth Sciences, the workshop "Mathematics and Geosciences: Global and Local Perspectives" was hold in Madrid at ICMAT from 4-8 November, 2013. This is the first volume of the Topical Issue on "Mathematics and Geosciences: Global and Local Perspectives" and contains 13 papers, most of which were presented at the congress. They address different topics under both global and local perspectives such as the percolation theory to observe micro seismicity in fracking, fractional differential analysis to model complex dynamics, climate change, earthquake statistics, earth rotation, geomagnetic field, fire models, Mars exploration, numerical methods in meteorology and environmental conservation, probabilistic models in study of soils and fluid mechanics. This volume addresses the interest of scientists of many of the branches in Earth Sciences as well as postgraduate students, covering both approaches, applied and theoretical ones, to solve different problems in Geosciences with the help of mathematical models and methods.