Longitudinal data (LD) occurs when repeated measurements from the same subject are observed overtime. In this book, exploratory data analysis (EDA)and models are utilized jointly to analyze LD which leads to stronger and better justified conclusions.Here we catalog the general principles of EDA for multivariate LD, and illustrate the use of the linked brushing approach for studying the mean structure over time. We also introduce models for multivariate longitudinal binary data: Marginalized transition random effects models (MTREM). These models exploit the marginal covariate effects while accounting for the dependence across time and responses. The methods are illustrated on several real datasets. It is possible to reveal the unexpected, to explore the interaction between responses and covariates, to observe the individual variations, and to understand structure in multiple dimensions by using these methods. The text includes visualization tools,detailed derivations for the models and computer code examples. This book will be of interest to students and researchers in (bio)statistics, social sciences and related fields.