Reliable analysis of the electromagnetic situation in a particular area is critical for wireless technology applications. With the increased number of devices and exploration of the new frequency bands, sensing helps, inter alia, in interference and radio resource management. Additionally, it facilitates the classification of signals to detect jammers and distinguish between legal and anomalous transmitters. This paper discusses the cooperative sensor network as a technology candidate for 6G. Specifically, we describe a possible architectural extension of the future cellular networks to obtain and utilize spectrum awareness. Several applications are systematically reviewed in this context, including dynamic spectrum sharing for coexistence in unlicensed bands, spectrum monitoring for signal detection and classification, and emitter localization. Qualitative and quantitative examples of possible performance improvements in cellular networks with the proposed approach are presented. Finally, we highlight the open research topics and challenges to solve for such a cooperative sensor network.