Enabling technologies of 5G and beyond wireless communication networks, such as millimeter-wave communication, beamforming, and multiple-input multiple-output (MIMO) antenna systems, are becoming increasingly dependent on accurate information of the physical environment for optimized communication performance. The acquisition of this information is a significant challenge, which can be eased by knowledge of the radio environment. Radio environment mapping (REM) has long been considered an enabler of cognitive radios (CRs). However, the limitations of radios effectively confined the application of REM to spectrum sensing and interference mapping. With the advent of more capable software-defined radios and advanced networks, the idea of a truly intelligent communication system empowered by enhanced REM can be realized. To this effect, we propose the generalized radio environment monitoring (G-REM) concept to include all aspects of the radio environment. We outline a general, self contained framework which enables radio environment monitoring in standalone devices. The presented G-REM framework comprises of different information sources, sensing methods, sensing modes, and mapping techniques to enable the realization of more reliable, secure, efficient, and faster future wireless networks. The accompanying challenges and future research direction are also provided.