We provide the description, mathematical formulation and illustrative results of the World Gas Model, a multi-period complementarity model for the global natural gas market with explicit consideration of market power in the upstream market. Market players include producers, traders, pipeline and storage operators, LNG (liquefied natural gas) 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 model is calibrated to match production and consumption projections from the PRIMES [EC. European energy and transport: trends to 2030-update 2007. Brussels: European Commission; 2008] and POLES models [EC. World energy technology outlook - 2050 (WETO-H2). Brussels: European Commission; 2006] up to 2030. The results of our numerical simulations illustrate how the supply shares of pipeline and LNG in various regions in the world develop very differently over time. LNG will continue to play a major role in the Asian market, also for new importers like China and India. Europe will expand its pipeline import capacities benefiting from its relative proximity to major gas suppliers.