Bounds on the capacity of wireless networks often rely on simplifying assumptions and are given in terms of coarse network parameters such as the number of nodes. While useful due to their simplicity such bounds can significantly overestimate the achievable capacity in real world situations, ignoring actual network topology and traffic patterns. The results of this paper improve such analytical results on network capacity in several ways. At the heart of our methodology lies the concept of transmission arenas which indicate the presence of active transmissions near any given location in the network. This novel space-based approach is well suited to untangle the interactions of simultaneous transmissions. Avoiding a graph-based model of the network it opens new avenues of studying capacities. For homogeneous networks we recover classical bounds. However, our methodology applies to arbitrary networks and can, thus, inform placing and activating of nodes also in the presence of clustering. Our method works with all classical channel models and dimensions. It provides bounds on the transport capacity which involve only high level knowledge of node locations, such as the length of Euclidean Minimum Spanning Tree. As an additional novelty we establish bounds on wireless unicast and multicast capacities.