Network and information systems are developed as the core of key infrastructures, economy and society. Once such systems are attacked by adversaries or severe security events, the security of national economy and the common value of the society can suffer from adverse impacts. Hence, how to detect network threats and how to ensure the security of network infrastructure are vital for protecting key technologies and constructing national cybersecurity assurance systems. We systematically review several studies on intrusion detection framework, automatic signature generation, security detection theories and methods, network topology monitoring and routing control. Furthermore, we summarize several scientific findings, such as cybersecurity detection algorithm and framework, wireless network security detection, network monitoring and security enhancement. Finally, we discuss several interesting future directions on cybersecurity detection and control.