Singular systems, also referred as implicit systems or descriptor systems, arise in many applications in practice such as electrical circuits, constrained robot systems, which can describe a larger class of systems other than the normal linear system model. In recent years, considerable amount of research concerning singular systems has been developed in the literature. It is well acknowledged that a linear singular system may possess impulsive modes and a non-singular transfer function, which is remarkably different from a non-singular system. In addition, a solution for the singular system with time-varying uncertainties may not exist even though the system is regular and impulse-free (or causal for discrete-time case). Furthermore, due to the physical constraints, limited capacity communication, the occurrences of abrupt structure or parameter variations and etc., the actuator saturation, data quantization and multi-mode switching are often encountered in practical control systems, which lead some fundamental and challenging issue to be investigated for singular systems. In this talk, we will present the recent advances of our research group in the study of singular systems, including the existence of solution, observer design and stabilization for nonlinear descriptor systems, detection and stabilization for networked singular systems, stability analysis of switched singular systems, etc. Finally, the application to consensus of nonlinear singular multi-agent systems under signed digraph is discussed.