This paper provides a comprehensive survey of clustering algorithms, categorizing them into traditional and modern methods. It discusses the definitions, key concepts, and evaluation criteria of clustering, and analyzes various clustering algorithms from two perspectives: traditional and modern. Traditional clustering algorithms include partition-based, hierarchical, fuzzy, distribution-based, density-based, graph-based, grid-based, fractal-based, and model-based methods. Modern clustering algorithms include kernel-based, ensemble-based, swarm intelligence-based, quantum-based, spectral graph theory-based, affinity propagation-based, density and distance-based, spatial data-based, data stream-based, and large-scale data-based methods. Each algorithm is analyzed in terms of its time complexity, advantages, and disadvantages. The paper highlights the importance of selecting appropriate clustering algorithms based on the characteristics of the data and the requirements of the application. It also discusses the challenges and limitations of different clustering approaches, such as sensitivity to parameters, scalability, and the ability to handle non-convex data. The paper concludes that clustering is a fundamental technique in data analysis, and the choice of algorithm depends on the specific problem and data characteristics. The paper also emphasizes the need for further research in this area to develop more efficient and effective clustering methods.This paper provides a comprehensive survey of clustering algorithms, categorizing them into traditional and modern methods. It discusses the definitions, key concepts, and evaluation criteria of clustering, and analyzes various clustering algorithms from two perspectives: traditional and modern. Traditional clustering algorithms include partition-based, hierarchical, fuzzy, distribution-based, density-based, graph-based, grid-based, fractal-based, and model-based methods. Modern clustering algorithms include kernel-based, ensemble-based, swarm intelligence-based, quantum-based, spectral graph theory-based, affinity propagation-based, density and distance-based, spatial data-based, data stream-based, and large-scale data-based methods. Each algorithm is analyzed in terms of its time complexity, advantages, and disadvantages. The paper highlights the importance of selecting appropriate clustering algorithms based on the characteristics of the data and the requirements of the application. It also discusses the challenges and limitations of different clustering approaches, such as sensitivity to parameters, scalability, and the ability to handle non-convex data. The paper concludes that clustering is a fundamental technique in data analysis, and the choice of algorithm depends on the specific problem and data characteristics. The paper also emphasizes the need for further research in this area to develop more efficient and effective clustering methods.