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We define and study capacity regions for ad hoc wireless networks with an arbitrary number of nodes and topology. These regions describe the set of achievable rate combinations between all source-destination pairs in the network under various transmission strategies, such as variable rate transmission, single hop or multihop routing, power control, and successive interference cancellation. With slight modifications, the developed formulation can handle multihop cellular networks, time-varying flat-fading channels and node mobility. Numerical results indicate that multihop routing, spatial reuse, and successive interference cancellation significantly increase the capacity of the network. On the other hand, gains by power control are not significant when the transmission rate is adapted to the channel SINR. We also find that time-varying flat fading and node mobility improve the performance of the network. Similar trends are observed for the special case of multihop cellular networks.