Cognitive radio provides a feasible solution for alleviating the lack of spectrum resources by enabling secondary users to access the unused spectrum dynamically. Spectrum sensing and learning, as the fundamental function for dynamic spectrum sharing in 5G evolution and 6G wireless systems, have been research hotspots worldwide. This paper reviews classic narrowband and wideband spectrum sensing and learning algorithms. The sub-sampling framework and recovery algorithms based on compressed sensing theory and their hardware implementation are discussed under the trend of high channel bandwidth and large capacity to be deployed in 5G evolution and 6G communication systems. This paper also investigates and summarizes the recent progress in machine learning for spectrum sensing technology.