The operation of unmanned aerial vehicles (UAV) imposes various challenges on radio spectrum management to achieve safe operation, efficient spectrum utilization, and coexistence with legacy wireless networks. Current spectrum schemes have limitations when applied to UAV networks due to the dynamic nature of UAV networks that require adaptive spectrum decisions and robust schemes that provide seamless and reliable services. Existing surveys mostly focus on UAV applications, channel models, and security challenges, with a lack of studies on spectrum management in the context of UAV networks. Further, current spectrum efforts focus on terrestrial networks that feature fixed infrastructure and less dynamicity as compared to UAV networks. This motivates the need to revisit existing approaches and identify suitable schemes that allow for the rapid integration of UAVs with existing wireless technologies. Motivated by this observation, this article presents a comprehensive survey on spectrum management for UAV operations. It identifies suitable management schemes that align with UAV features and requirements to enable safe and efficient usage of the radio spectrum. The article assumes coexistence with prevalent wireless technologies that occupy the spectrum. It first presents the ruling from policymakers and regulators and discusses operation bands and radio interfaces. It then introduces deployment scenarios (applications and architectures) as standalone or heterogeneous networks. This is followed by a systematic structure for the management tools that employ deterministic, opportunistic, and competitive schemes. In addition, network monitoring, patrolling, and enforcement schemes are identified. The survey also specifies key tools that can be leveraged for spectrum management solutions such as optimization and blockchain. Finally, it recognizes open research directions and challenges that need to be tackled to advance UAV communications.