The Network-on-Chip (NoC) paradigm has emerged as a scalable interconnection infrastructure for modern multicore chips. However, with growing levels of integration, the traditional NoCs suffer from high latency and energy dissipation in on-chip data transfer due to conventional multihop metal/dielectric-based interconnects. Three-dimensional integration, on-chip photonics, RF, and wireless links have been proposed as radical low-power and low-latency alternatives to the conventional planar wire-based designs. Wireless NoCs with Carbon NanoTube (CNT) antennas are shown to outperform traditional wire-based NoCs significantly in achievable data rate and energy dissipation. However, such emerging and transformative technologies will be prone to high levels of failures due to various issues related to manufacturing challenges and integration. On the other hand, several naturally occurring complex networks such as colonies of microbes and the World Wide Web are known to be inherently robust against high rates of failures and harsh environments. This article advocates adoption of such complex network-based architectures to minimize the effect of wireless link failures on the performance of the NoC. Through cycle-accurate simulations it is shown that the wireless NoC architectures inspired by natural complex networks perform better than their conventional wired counterparts even in the presence of high degrees of link failures. We demonstrate the robustness of the proposed wireless NoC architecture by incorporating both uniform and application-specific traffic patterns.