Fuzzy partitional clustering algorithms are widely used in pattern recognition field. Until now, more and more research results on them have been developed in the literature. In order to study these algorithms systematically and deeply, they are reviewed in this paper based on c-means algorithm, from metrics, entropy, and constraints on membership function or cluster centers. Moreover, the advantages and disadvantages of the typical fuzzy partitional algorithms are discussed. It is pointed out that the standard FCM algorithm is robust to the scaling transformation of dataset, while others are sensitive to such transformation. Such conclusion is experimentally verified when implementing the standard FCM and the maximum entropy clustering algorithm. Finally, the problems existing in these algorithms and the prospects of the fuzzy partitional algorithms are discussed.