Satellite remote sensing is becoming an increasingly essential component of volcano monitoring, especially at little-known and remote volcanoes where in-situ measurements are unavailable and/or impractical. Moreover the synoptic view captured by satellite imagery over volcanoes can benefit hazard monitoring efforts. By monitoring, we mean both following the changing styles and intensities of the eruption once it has started, as well as nowcasting and eventually forecasting the areas potentially threatened by hazardous phenomena in an eruptive scenario. Here we demonstrate how the diversity of remote sensing data over volcanoes and the mutual interconnection between satellite observations and numerical simulations can improve lava flow hazard monitoring in response to effusive eruption. Time-averaged discharge rates (TADRs) obtained from low spatial/high temporal resolution satellite data (e.g. MODIS, SEVIRI) are complemented, compared and fine-tuned with detailed maps of volcanic deposits with the aim of constraining the conversion from satellite-derived radiant heat flux to TADR. Maps of volcanic deposits include the time-varying evolution of lava flow emplacement derived from multispectral satellite data (e.g. EO-ALI, Landsat, Sentinel-2, ASTER), as well as the flow thickness variations, retrieved from the topographic monitoring by using stereo or tri-stereo optical data (e.g. Pléiades, PlanetScope, ASTER). Finally, satellite-derived parameters are used as input and validation tags for the numerical modelling of lava flow scenarios. Here we show how our strategy was successfully applied to several remote volcanoes around the world.