The spectrum cartography finds applications in several areas such as cognitive radios, spectrum aware communications, machine-type communications, Internet of Things, connected vehicles, wireless sensor networks, and radio frequency management systems, etc. This paper presents a survey on state-of-the-art of spectrum cartography techniques for the construction of various radio environment maps (REMs). Following a brief overview on spectrum cartography, various techniques considered to construct the REMs such as channel gain map, power spectral density map, power map, spectrum map, power propagation map, radio frequency map, and interference map are reviewed. In this paper, we compare the performance of the different spectrum cartography methods in terms of mean absolute error, mean square error, normalized mean square error, and root mean square error. The information presented in this paper aims to serve as a practical reference guide for various spectrum cartography methods for constructing different REMs. Finally, some of the open issues and challenges for future research and development are discussed. © 2021 The Authors