Clustering is one of the data mining methods. In all clustering algorithms, the goal is to minimize intracluster distances, and to maximize intercluster distances. Whatever a clustering algorithm provides a better performance, it has the more successful to achieve this goal. Nowadays, although many research done in the field of clustering algorithms, these algorithms have the challenges such as processing time, scalability, accuracy, etc. Comparing various methods of the clustering, the contributions of the recent researches focused on solving the clustering challenges of the partition method. In this paper, the partitioning clustering method is introduced, the procedure of the clustering algorithms is described, and finally the new improved methods and the proposed solutions to solve these challenges are explained.