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We develop bounds on the capacity of wireless multihop networks when the traffic pattern is non-uniform, i.e., not all nodes are the sources and sinks of similar volumes of traffic. Our results are asymptotic, i.e., they hold with probability going to unity as the number of nodes goes to infinity. We study (i) asymmetric networks, where the numbers of sources and destinations of traffic are unequal, (ii) multicast networks, in which each created packet has multiple destinations, (Hi) cluster networks, that consist of clients and a limited number of cluster heads, and each client wants to communicate with any one of the cluster heads, and (iv) hybrid networks, in which the nodes are supported by a limited infrastructure. Our findings quantify the fundamental capabilities of these wireless multihop networks to handle traffic bottlenecks, and point to correct design principles that achieve the capacity without resorting to overly complicated protocols.