Longitudinal data occurs when repeated measurements from the same subject are observed over time. In this thesis, exploratory data analysis and models are utilized jointly to analyze longitudinal data which leads to stronger and better justified conclusions. The complex structure of longitudinal data with covariates requires new visual methods that enable interactive exploration. Here we catalog the general principles of exploratory data analysis for multivariate longitudinal data, and illustrate the use of the linked brushing approach for studying the mean structure over time. It is possible to reveal the unexpected, to explore the interaction between responses and covariates, to observe the individual variations, understand structure in multiple dimensions, and diagnose and fix models by using these methods. We also propose models for multivariate longitudinal binary data that directly model marginal covariate effects while accounting for the dependence across time via a transition structure and across responses within a subject for a given time via random effects. Markov Chain Monte Carlo Methods, specifically Gibbs sampling with Hybrid steps, are used to sample from the posterior distribution of parameters. Graphical and quantitative checks are used to assess model fit. The methods are illustrated on several real datasets, primarily the Iowa Youth and Families Project.*;*This dissertation is a compound document (contains both a paper copy and a CD as part of the dissertation).