Unmanned aerial vehicle (UAV)-enabled integrated sensing and communication (ISAC) has attracted growing research interests in the context of sixth-generation (6G) wireless networks, in which UAVs will be exploited as aerial wireless platforms to provide better coverage and enhanced sensing and communication (S&C) services. However, due to the size, weight, and power (SWAP) constraints of UAVs, their controllable mobility, and the line-of-sight (LoS) air-ground channels, UAV-enabled ISAC introduces new opportunities and challenges. This article provides an overview of UAV-enabled ISAC and proposes various solutions for optimizing the S&C performance. In particular, we first introduce UAV-enabled joint S&C and discuss UAV motion control, wireless resource allocation, and interference management for ISAC systems employing single and multiple UAVs. Then, we present two application scenarios for exploiting the synergy between S&C, namely sensing-assisted UAV communication and communication-assisted UAV sensing. Finally, we highlight several interesting research directions to guide and motivate future work.