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Finsler Spacetimes, Observers and Applications In classical relativity theory, different observers measure space and time and their measurements are coherent in a precise way (related by Lorentz transformations). However, in trying to unify relativity with quantum theory, small anisotropies may be introduced on spacetime, and their effects may add up to break the classical Lorentz symmetry. This gives rise to Finsler spacetimes. After covering their geometric foundations, we will discuss their surprisingly large array of applications. First, we will comment on anisotropic propagation of signals and, particularly, the refined modelling of wildfires. Then, we will focus on recently studied new phenomena in cosmology. These have the potential to explain measurements such as the accelerated expansion of the universe as purely geometrical effects, without the need of introducing dark energy or dark matter. Fidel Fernández Villaseñor is at the University of Granada, Joint work with, Miguel Sánchez (Univ. of Granada) and Miguel Ángel Javaloyes (University of Murcia)