Adaptive equalization algorithms play a pivotal role in suppressing inter-symbol interference in wireless channels. Contemporarily, with the rapid development of science and technology, there is still a lack of unified cognition for adaptive equalization algorithms. Therefore, this study systematically discusses the research status and development process of adaptive equalization algorithms, focusing on the least mean square algorithm (LMS), constant modulus blind equalization algorithm (CMA) and neural network algorithm. Subsequently, based on Matlab simulation, their performance is analyzed visually. Finally, a table is listed to compare the three commonly used algorithms. From the aspects of practicability and application environment, it deeply analyzes the limitations of traditional adaptive equalization algorithms such as LMS and CMA in the current era, and demonstrates the superior performance of neural networks. On this basis, this paper emphasizes the powerful learning ability of neural networks and the opportunities for future research, which will lay the foundation for the development of next-generation communication networks.