Quantifying lava flow hazards by combining field observations, satellite data and numerical modelling has immediate applications to the real time monitoring of effusive eruptions, including both following the manifestations of the eruption once it has started as well as forecasting the areas potentially threatened by lava. Although the scientific community has been striving to develop numerical models that adopt a more complete description of the physical processes governing the lava flow dynamics and emplacement, the overall uncertainty in projecting lava inundation hazards has not been reduced. Lava flow emplacement is sensitive to several factors such as effusion rate, the changing rheology of molten lava as it cools down-flow, and topographic attributes of the terrain. This is reflected in physics-based models through their sensitivity to input parameters, so that propagation of error through a simulated flow may have a significant effect on its accuracy and reliability. Hence, projections based on such models should be provided with a quantification of the uncertainties and their impact on the accuracy of the results. A comprehensive approach to hazard monitoring during effusive eruptions can only result by bringing together new knowledge from field observations, sample return and analysis, remote sensing, experimental measurements, physical modelling, and computer simulations. Specific topics to be discussed will include: (i) describing field and remote sensing data provisions and their sources of uncertainty, (ii) evaluating model robustness through validation against real case studies, and (iii) model comparison between numerical simulations, analytical solutions and laboratory experiments, as well as (iv) quantification of uncertainty propagation through both forward (sensitivity analyses) and inverse (optimization/calibration) modelling in all components of lava flow hazard modelling in response to effusive crisis.