The applicability of linear regression analysis hinges on the presumption that the dataset enjoys a single linear model. In reality, however, a dataset may admit multiple groups, each of which assumes a distinct model. In real data analysis, this subgroup structure involving functional heterogeneity is generally unknown. A suite of methodologies has been developed to unravel such subgroup structure. The proposed methods have wide applications in various fields (e.g., marketing, agriculture and clinical trials).