Longitudinal data arise frequently in biomedical and health studies, where each subject is repeatedly measured over time. For instance, a randomized controlled trial was conducted in the Washington, D.C. area from March 1997 through May 2002 of 267 women with current major depression. In this study, one of three treatments was randomly assigned to each participant, namely cognitive behavior therapy (CBT), antidepressant medication, and referral to community care. Longitudinal data have been used to compare the treatments and assess the response of each treatment on a patient over time with the goal being to find the most effective treatment. In this talk, various statistical models for longitudinal data will be introduced to address the aforementioned goal of the study: 1) Multiple linear regression model; 2) Personalized treatment effect model; 3) Initial severity-dependent model; 4) Generalized growth curve mean model; 5) Growth curve quantile model.