The expectation-maximization (EM) algorithm is highly popular in computational statistics because it possesses a number of desirable properties such as reliable global convergence, numerical stability, and simplicity of implementation. More complex data are now increasingly prevalent across many application areas in a wide scope of scientific fields. These data could exhibit a hierarchical or longitudinal structure and involve atypical and/or asymmetric observations. The application of the EM algorithm in the analysis of these complex data presents significant challenges to existing EM methods. It is because the models developed often lead to intractable expectation-steps or complicated maximization-steps in order to model the correlation between hierarchical data and/or the skewness of asymmetric observations. This paper discusses recent advanced developments in EM methods to overcome these barriers in handling complex problems.