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Lava flows rarely present a risk for populations, but they are one of the most frequent volcanic hazards on a global scale and devastate absolutely everything on their path. Monitoring and anticipating the trajectory of lava flows is therefore the best approach to reduce losses and mitigate the risks associated with this phenomenon. Lava flow emplacement dynamics (speed, rheological behavior, morphology, length) depend mainly on the topography, the volumetric flow at the vent, the volume emitted, and the rheology of the lava itself. Lava rheology is directly linked to temperature, chemical composition and to petrology (major element composition, redox state, volatile content, and shape and size of bubbles and crystals). During flowing, upon cooling the thermal gradient along and across the flow evolves continuously and triggers crystallization associated with evolution of the residual liquid chemical composition. This dynamic process has a direct influence on lava viscosity, which lets the flow to stop when rheological parameters are such they impede further motion. We present here how lava viscosity is measured in the lab and in the field and how its evolution down flow may be modelled. To anticipate lava flow trajectory and maximum length, we then set up a protocol that merges a stochastic approach to model the flood zone and a thermo-rheological model to calculate the distance reached as a function of the effusion rate. Using almost real-time satellite data, we apply this protocol to monitor and anticipate the advance of lava flows at Piton de la Fournaise.