In this article, we show two topics of the EM (expectation-maximization) algorithm. One is the Wake-Sleep (W-S) algorithm which is proposed by P. Dayan and G. Hinton. The algorithm was believed to converge by the similarity between W-S and EM algorithms. But we have clarified that they are different and the convergence is not clear in general cases. The other topic is the recursive EM algorithm. This algorithm approximate the Fisher’s scoring method by using the EM algorithm recursively and tries to accelerate the EM algorithm. We show the background of the algorithm and some numerical simulations.