As new and interesting peer-to-peer applications combine with advancements in networking technology, they are reaching millions of users across the globe. Numerous studies have shown, however, that loss of connectivity is common on the wide-area network, due to hardware and software failures, and network misconfigurations. Despite the natural redundancy present in underlying network links, the current IP layer fails to recognize and recover from these frequent failures in a timely fashion. This paper presents fault-tolerant routing on the Tapestry overlay network, which exploits existing network redundancy by dynamically switching traffic onto precomputed alternate routes. Furthermore, messages in our system can be duplicated and multicast "around" network congestion and failure hotspots with rapid reconvergence to drop duplicates. Our simulations show fault-tolerant Tapestry to be highly effective at circumventing link and node failures, with reasonable cost in terms of additional routing latency and bandwidth cost.