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Machine learning (ML) algorithms have been widely used to improve the performance of telecommunications systems, including reconfigurable intelligent surface (RIS)-assisted wireless communication systems. The RIS can be considered a key part of the backbone of sixth-generation (6G) communication mainly due to its electromagnetic properties for controlling the propagation of the signals in the wireless channel. The ML-optimized (RIS)-assisted wireless communication systems can be an effective alternative to mitigate the degradation suffered by the signal in the wireless channel, providing significant advantages in the system's performance. However, the variety of approaches, system configurations, and channel conditions make it difficult to determine the best technique or group of techniques for effectively implementing an optimal solution. This paper presents a comprehensive review of the reported frameworks in the literature that apply ML and RISs to improve the overall performance of the wireless communication system. This paper compares the ML strategies that can be used to address the RIS-assisted system design. The systems are classified according to the ML method, the databases used, the implementation complexity, and the reported performance gains. Finally, we shed light on the challenges and opportunities in designing and implementing future RIS-assisted wireless communication systems based on ML strategies. [ABSTRACT FROM AUTHOR]