Networks of nanoscale conductors such as carbon nanotubes, graphene, and metallic nanowires are promising candidates to replace metal oxides as transparent conductors. However, very few previous reports have described nanostructured thin films that reach the standards required by industry for high-performance transparent electrodes. In this review, we analyze the sheet resistance and transmittance data extracted from published literature for solution processed, nanostructured networks. In the majority of cases, as their thickness is reduced below a critical value, nanoconductor networks undergo a transition from bulk-like to percolative behavior. Such percolative behavior is characteristic of sparse networks with limited connectivity and few continuous conductive paths. This transition tends to occur for films with a transmittance between 50% and 90%, which means that the properties of highly transparent films are predominately limited by percolation. Consequently, to achieve low resistance coupled with high transparency, the networks must be much more conductive than would otherwise be the case. We show that highly conductive networks of metallic nanowires appear to be the most promising candidate to replace traditional transparent electrode materials from a technical standpoint. However, many other factors, including cost, manufacturability, and stability, will have to be addressed before commercialization of these materials.