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Intelligent signal processing for wireless communications is a vital task in modern wireless systems, but it faces new challenges because of network heterogeneity, diverse service requirements, a massive number of connections, and various radio characteristics. Owing to recent advancements in big data and computing technologies, artificial intelligence (AI) has become a useful tool for radio signal processing and has enabled the realization of intelligent radio signal processing. This survey covers four intelligent signal processing topics for the wireless physical layer, including modulation classification, signal detection, beamforming, and channel estimation. In particular, each theme is presented in a dedicated section, starting with the most fundamental principles, followed by a review of up-to-date studies and a summary. To provide the necessary background, we first present a brief overview of AI techniques such as machine learning, deep learning, and federated learning. Finally, we highlight a number of research challenges and future directions in the area of intelligent radio signal processing. We expect this survey to be a good source of information for anyone interested in intelligent radio signal processing, and the perspectives we provide therein will stimulate many more novel ideas and contributions in the future.