This chapter considers some examples of the use of the expectation-maximization (EM) algorithm. It also considers a fairly general formulation of the self-consistency concept for likelihoods obtained from grouped multinomial data. Despite the concavity of the log likelihood, convergence of the EM algorithm to a maximum likelihood estimate is not guaranteed, due to possible anomalous behaviour on the boundaries of the parameter space. The EM algorithm can cope with the nonparametric estimation of EMa distribution function from survival times subject to both left and right censoring. For truncated data, a slight modification of the algorithm is needed, but the important special case of left truncation combined with right censoring has a simple explicit solution. The chapter concludes with a brief comparison of the EM algorithm with its main competitor, direct maximization by the Newton–Raphson procedure.