Comment: 54 pages, 1 figureThis paper develops a new model and estimation procedure for panel data that allows us to identify heterogeneous structural breaks. We model individual heterogeneity using a grouped pattern. For each group, we allow common structural breaks in the coefficients. However, the number, timing, and size of these breaks can differ across groups. We develop a hybrid estimation procedure of the grouped fixed effects approach and adaptive group fused Lasso. We show that our method can consistently identify the latent group structure, detect structural breaks, and estimate the regression parameters. Monte Carlo results demonstrate the good performance of the proposed method in finite samples. An empirical application to the relationship between income and democracy illustrates the importance of considering heterogeneous structural breaks.