Due to the rapid growth in data and access to various data sources, data has become complex and heterogeneous in many fields. It is thus necessary to discover the meaningful underlying structure of such data, which is possibly low-dimensional. In this dissertation, we propose reduced rank mixture models for multivariate response regression, which simultaneously address data heterogeneity and the low-rankness of coefficient matrices. The proposed approach provides more parsimonious and interpretable models as an extension of finite mixture models to reduced rank regression. We show the complete derivation of computationally efficient algorithms that simultaneously perform subgroup identification, parameter estimation, and rank determination. Via the proposed paradigm, we have some desired features such as the monotonicity of the penalized likelihood sequence. The asymptotic consistency of the proposed estimators is also established. In addition to the theoretical foundations, simulation studies and real data analysis have been carried out to show the effectiveness and practical usefulness of the proposed methods. The R package rrMixture is developed for the implementation and is publicly available on CRAN.