The idea of this special issue comes out of discussions at the workshop on "Uncertainty Quantification in Lava Flow Hazard Modeling and Real-Time Source Term Provision" held at the Istituto Nazionale di Geofisica e Vulcanologia (INGV) in Catania (Italy) during February 2017. The workshop was supported by the MeMoVolc network of the European Science Foundation, and was attended by delegates from Italy, France, UK, Germany, Spain, and the USA. At the workshop, researchers expert in lava's physical properties, satellite volcano hot spot detection, lava flow modeling, and effusive crisis response were brought together to share experiences and perspectives on the current capabilities in application of remote sensing and modeling to better forecast hazards during effusive eruptions. In addition, the workshop led to a community-wide agreement that many scientific uncertainties still need to be resolved in model-based hazard assessments, and this requires support through the creation of a special working group. This special issue consists of 15 papers focused largely on the conclusions of the MeMoVolc workshop, as follows.