Unlike ordinary differential systems, delayed systems do not have a mature investigation method, making its analysis and control very hard. Meanwhile, delay widely exists in systems of neural networks, artificial intelligence, machining, multi agents, robotic control, which enhances the significance of studies of timedelayed systems. Therefore, this special issue focuses on the problems of stability, nonlinear dynamics and control determined by time delay, especially in neural systems, networks, machineries, and vibration mitigation with delays, expecting to provide some valuable references for scholars interested in related topics.