The human microbiome plays a crucial role in health and disease. Advances in next-generation sequencing technologies have made it possible to quantify microbiome composition with high resolution. Clustering microbiome data can uncover meaningful patterns across samples, offering insights into biological variability and disease mechanisms. However, this task presents several challenges. Microbiome data are typically high-dimensional, over-dispersed, and compositional, the latter meaning they reflect relative, not absolute, abundances. As such, analyzing such compositional data presents many challenges because they are restricted to a simplex, which complicates standard statistical analysis. Various mixture model-based approaches have been proposed previously. These models assume that the population is a finite mixture of subpopulations (or clusters), each characterized by a probability distribution. My research team has focused on developing and refining such models to improve clustering accuracy and interpretability. We will present recent contributions from our group, emphasizing the strengths and limitations of different component-specific distributions used within mixture models. For example, Dirichlet-multinomial (DM) mixture models are computationally efficient but often fail to capture the complex correlation structures present in microbiome data. In contrast, models based on the logistic normal multinomial (LNM) distribution provide greater flexibility in capturing correlations but are computationally intensive. To overcome these limitations, we have developed a computationally efficient framework for parameter estimation in LNM-based models using variational Gaussian approximations. This approach significantly reduces the computational burden and enables application to large-scale datasets. Some other recent and ongoing developments using extensions of the LNM distribution and others to cluster microbiome data will be discussed.