We provide the description and illustrative results of the World Gas Model, a multi-period complementarity model for the global natural gas market. Market players include producers, traders, pipeline and storage operators, LNG liquefiers and regasifiers as well as marketers. The model data set contains more than 80 countries and regions and covers 98% of world wide natural gas production and consumption. We also include a detailed representation of cross-border natural gas pipelines and constraints imposed by long-term contracts in the LNG market. The Base Case results of our numerical simulations show that the rush for LNG observed in the past years will not be sustained throughout 2030 and that Europe will continue to rely on pipeline gas for a large share of its imports and consumption.