Abstract: The existing finite mixture modeling and model-based clustering literature focuses primarily on the analysis of multivariate data observed in the form of vectors, with each element representing a specific feature. In this setting, multivariate Gaussian mixture models have been the most commonly used. Due to severe modeling issues observed when normal components cannot provide adequate fit to groups, much attention is paid to developing models capable of accounting for skewness in data. We target the problem of mixture modeling with components that can handle skewness in matrix- and tensor-valued data. The proposed developments open a wide range of possible modeling capabilities, with numerous applications, as illustrated in the talk.