Topological quantum computation provides an elegant way around decoherence, as one encodes quantum information in a non-local fashion that the environment finds difficult to corrupt. In this talk I will describe a surprising new topological quantum computation platform: one-dimensional semiconductor wire networks. Recent work [1] provides a recipe for driving semiconducting wires into a topological phase supporting long-sought particles known as Majorana fermions that can store topologically protected quantum information. Majorana fermions in this setting can be transported, created, and fused by applying locally tunable gates to the wire. More importantly [2], networks of such wires allow Majorana fermions to be meaningfully braided, exhibiting non-Abelian statistics like vortices in a p + ip superconductor. We propose experimental setups that allow for efficient exchange of arbitrary numbers of Majorana fermions. [1] Y. Oreg, G. Refael, F. von Oppen, Helical liquids and Majorana bound states in quantum wires, arXiv:1003.1145 [2] J. Alicea, Y. Oreg, G. Refael, F. von Oppen, M.P.A. Fisher, Non-Abelian statistics and topological quantum computation in 1D wire networks, arXiv:1006.4395