Transported Saharan dust creates a substantial natural background to particulate matter concentrations in Central Europe. The contributions by Saharan dust are especially detectable at Alpine mountain sites, where many other sources have little impact. The ability of a chemical weather forecasting model to simulate dust transport is of vital interest, as serious health effects due to this phenomenon, similar in scale to those resulting from nuclear or industrial accidents, wildfires, pollen, etc., may require countermeasures. Thus, we investigate whether the WRF-Chem model set-up, which is run operationally for air quality forecasts in Austria, can accurately predict the transport of the Saharan dust cloud towards Central Europe in April 2016. WRF-Chem simulations with and without desert dust emissions reveal that whenever PM concentrations were high during the three periods of this event, 60–70% of the dust arriving at the Eastern Alps originated in the desert. The measurements and model results deliver a detailed picture of the course of this extraordinary dust event, with successive peaks over the Eastern Alpine region. Using this long-lasting Saharan dust event as an example, a structured step-wise approach is proposed to investigate peak dust episodes based on data analysis of representative background sites, source area analysis by means of Lagrangian dispersion modelling, and coupled meteorological and chemical modelling.