Abstract: ‍ ‍In conventional clustering analysis， it is generally assumed that the correct or appropriate number of clusters in a given dataset is given in advance， otherwise， the clustering algorithms cannot lead to a reasonable clustering result. When a competitive learning （CL） algorithm is applied to clustering analysis， it is faced with the same problem. In fact， the selection of number of clusters （or competitive units in the CL algorithm） for a dataset is a very difficult problem. As for this difficult problem， Rival Penalized Competitive Learning （RPCL） algorithm provides an effective idea and method. By overestimating the number of clusters in the given dataset， it has the ability of automatically allocating an appropriate number of cluster centers in the data and pushing out the extra cluster centers far away to the infinity by adopting the rival penalized mechanism into the conventional competitive learning. This favourable idea and method has opened up a new way on clustering analysis. This paper reviews the developments and applications of RPCL algorithm， including the origin of its idea， mathematical derivation and analysis， generalized versions for different types of data， and various applications.