Several features may separately or in combination influence conduct and performance of an industry, e.g. the numbers of sellers or buyers, the degree of economies of scale in production and distribution, the temporal and spatial dimensions, etc. Our main focus is on how to model market power. In particular, we demonstrate the rather different solutions obtained from the price-taking behavior versus the oligopolistic Cournot behavior. We also consider two approaches to model the transportation of natural gas. Finally, there is a brief review of previous modeling efforts of the European natural gas industry.