Over the past decade, the integration of the Internet of Things (IoT), 5th Generation Mobile Networks (5G), and Cloud 3.0 technologies has significantly transformed the internet landscape. These advancements have led to a massive increase in connected devices and data generation. Traditional network management, reliant on manual processes and simple mathematical models, has become insufficient due to the increased complexity and dynamic nature of modern networks. To address these new challenges, self-running networks as an enhanced network management approach can be utilized. These networks are characterized by their autonomous and intelligent capabilities that remove the need for human intervention. This paper explores the core components and functionalities of self-running networks and proposes their architecture. Additionally, the paper highlights ongoing research toward self-running networks. Current challenges in implementing self-running networks, such as security, interoperability, orchestration, and complexity, are also discussed. We complete this paper by examining use cases for two types of networks-Data Center Networks (DCN) and Wireless Sensor Networks (WSN)-and illustrate how self-running networks can revolutionize their functionality and efficiency.