This paper provides a brief historical overview of linear singular systems, followed by a survey of their solution and properties. It discusses both frequency domain and time domain approaches to give an overall picture of the current state of the theory. Linear singular systems are described by equations of the form $ E\dot{x} = Ax + Bu $, where $ E $ is the Jacobian matrix with respect to $ \dot{x} $, and $ A $ is the Jacobian matrix with respect to $ x $. These systems can be singular when $ |E| = 0 $, meaning that they cannot be converted into a standard state variable system without losing information. Singular systems have applications in economics (e.g., the Leontieff model), demography (e.g., the Leslie model), and large-scale systems (e.g., power systems and interconnected systems). They also appear in robotics, neutral delay systems, aircraft dynamics, and neurological events. Singular systems are used to analyze catastrophic behavior and optimal control problems. Recent research has also focused on applying singular systems to network theory, as demonstrated by the example of a transistor network. The paper highlights the importance of singular systems in various fields and their potential for further research.This paper provides a brief historical overview of linear singular systems, followed by a survey of their solution and properties. It discusses both frequency domain and time domain approaches to give an overall picture of the current state of the theory. Linear singular systems are described by equations of the form $ E\dot{x} = Ax + Bu $, where $ E $ is the Jacobian matrix with respect to $ \dot{x} $, and $ A $ is the Jacobian matrix with respect to $ x $. These systems can be singular when $ |E| = 0 $, meaning that they cannot be converted into a standard state variable system without losing information. Singular systems have applications in economics (e.g., the Leontieff model), demography (e.g., the Leslie model), and large-scale systems (e.g., power systems and interconnected systems). They also appear in robotics, neutral delay systems, aircraft dynamics, and neurological events. Singular systems are used to analyze catastrophic behavior and optimal control problems. Recent research has also focused on applying singular systems to network theory, as demonstrated by the example of a transistor network. The paper highlights the importance of singular systems in various fields and their potential for further research.