The massive growth in mobile users and wireless technologies has resulted in increased data traffic and created demand for additional radio spectrum. This growing demand for radio spectrum has resulted in spectrum congestion and mandated the need for coexistence between radar and interfering communication emitters. To address the aforementioned issues, it is critical to review existing policies and evaluate new technologies that can utilize spectrum in an efficient and intelligent manner. Cognitive radio and cognitive radar are two promising technologies that exploit spectrum using dynamic spectrum access techniques. Additionally, introducing the bio-inspired concept ‘metacognition’ in a cognitive process has shown to increase the effectiveness and robustness of the cognitive radio and cognitive radar system. Metacognition is a high-order thinking agent that monitors and regulates the cognition process through a feedback and control process called the perception–action cycle. Extensive research has been done in the field of spectrum sensing in cognitive radio and spectral coexistence between radar and communication systems. This paper provides a detailed classification of spectrum sensing schemes and explains how dynamic spectrum access strategies share the spectrum between radar and communication systems. In addition to this, the fundamentals of cognitive radio, its architecture, spectrum management framework, and metacognition concept in radar are discussed. Furthermore, this paper presents various research issues, challenges, and future research directions associated with spectrum sensing in cognitive radar and dynamic spectrum access strategies in cognitive radar. © 2022 Elsevier B.V.