This document summarizes research on efficient router designs for networks-on-chip (NOCs). It surveys several router architectures that aim to improve performance and energy efficiency, including a flexible router that handles requests to busy buffers, a hybrid two-layer router that supports both packet-switched and circuit-switched communications, and a clockless router called MANGO that provides guaranteed services. Fault tolerance is also addressed through simulation-based analysis of transient faults in NOC routers. The document surveys these efficient router designs for high-performance NOCs while balancing the tradeoff between area, power, and performance.