UAVs have rapidly become prevalent in applications related to surveillance, military operations, and disaster relief. Their low cost, operational flexibility, and unmanned capabilities make them ideal for accomplishing tasks in areas deemed dangerous for humans to enter. They can also accomplish previous high-cost and labor-intensive tasks, such as land surveying, in a faster and cheaper manner. Researchers studying UAV applications have realized that a swarm of UAVs working collaboratively on tasks can achieve better results. The dynamic work environment of UAVs makes controlling the vehicles a challenge. This is magnified by using multiple agents in a swarm. Resiliency is a broad concept that effectively defines how well a system handles disruptions in its normal functioning. The task of building resilient swarms has been attempted by researchers for the past decade. However, research on current trends shows gaps in swarm designs that make evaluating the resiliency of such swarms less than ideal. The authors believe that a complete well-defined system built from the ground up is the solution. This survey evaluates existing literature on resilient multi-UAV systems and lays down the groundwork for how best to develop a truly resilient system.