Over the past decade, unmanned aerial vehicles (UAVs) have demonstrated increasing attention and promise. They demonstrate great potential for application in both civilian and military fields. In this context, collision-avoidance (CA) approaches play an extremely important role in collaborative and noncollaborative UAVs in a common airspace for reliable and safe operation. In this article, we give an analysis and description of the CA functions, including the CA process, state sensing, conflict detection, and conflict resolution. Then, an overview of the recent progress in CA technologies is systematically provided, particularly in terms of sensing techniques, conflict detection, and conflict resolution. The state-sensing methods include ground-based and air-based sensing technologies, and cooperative and non-cooperative sensing. The conflict-detection methods contain conflict detection with certainty and without certainty. The conflict-resolution methods include methods for individual UAVs and for UAV formation. In addition, several challenging problems are introduced to develop a lucid research direction. This review gives a unique perspective and contributes toward the further development of CA approaches for UAVs.