Uncrewed aerial vehicle (UAV) swarms are pivotal in the applications such as disaster relief, aerial base station (BS) and logistics transportation. These scenarios require the capabilities in accurate sensing, efficient communication and flexible control for real-time and reliable task execution. However, sensing, communication and control are studied independently in traditional research, which limits the overall performance of UAV swarms. To overcome this disadvantage, we propose a deeply coupled scheme of integrated sensing, communication and control (ISCC) for UAV swarms, which is a systemic paradigm that transcends traditional isolated designs of sensing, communication and control by establishing a tightly-coupled closed-loop through the co-optimization of sensing, communication and control. In this article, we firstly analyze the requirements of scenarios and key performance metrics. Subsequently, the enabling technologies are proposed, including communication-and-control-enhanced sensing, sensing-and-control-enhanced communication, and sensing-and-communication-enhanced control. Simulation results validate the performance of the proposed ISCC framework, demonstrating its application potential in the future.