Longitudinal data (LD) occurs when repeatedmeasurements from the same subject are observed overtime. In this book, exploratory data analysis (EDA)and models are utilized jointly to analyze LD whichleads to stronger and better justified conclusions.Here we catalog the general principles of EDA formultivariate LD, and illustrate the use of the linkedbrushing approach for studying the mean structureover time. We also introduce models for multivariatelongitudinal binary data: Marginalized transitionrandom effects models (MTREM). These models exploitthe marginal covariate effects while accounting forthe dependence across time and responses. The methodsare illustrated on several real datasets. It ispossible to reveal the unexpected, to explore theinteraction between responses and covariates, toobserve the individual variations, and to understandstructure in multiple dimensions by using thesemethods. The text includes visualization tools,detailed derivations for the models and computer codeexamples. This book will be of interest to studentsand researchers in (bio)statistics, social sciencesand related fields.