This paper provides a historical overview of linear singular systems, followed by a survey of their solutions and properties. It discusses both frequency domain and time domain approaches to provide an comprehensive understanding of the current state of the theory. The introduction explains the form of implicit differential equations and the conditions under which they become singular. Special cases, such as singularly perturbed systems, are also discussed, highlighting the importance of considering both slow and fast subsystems. The paper emphasizes the applications of singular systems in various fields, including economics, demography, power systems, and interconnected systems. Recent applications in robotics, neutral delay systems, aircraft dynamics, and network theory are also mentioned, showcasing the versatility and relevance of singular systems in modern research and practical problems.This paper provides a historical overview of linear singular systems, followed by a survey of their solutions and properties. It discusses both frequency domain and time domain approaches to provide an comprehensive understanding of the current state of the theory. The introduction explains the form of implicit differential equations and the conditions under which they become singular. Special cases, such as singularly perturbed systems, are also discussed, highlighting the importance of considering both slow and fast subsystems. The paper emphasizes the applications of singular systems in various fields, including economics, demography, power systems, and interconnected systems. Recent applications in robotics, neutral delay systems, aircraft dynamics, and network theory are also mentioned, showcasing the versatility and relevance of singular systems in modern research and practical problems.