This chapter considers extensions of joint models to multidimensional longitudinal and/or survival data. The approaches covered here are useful for studies that collect information on more than one longitudinal outcome or event on each participant. For example, when studying the profiles of cognitive aging in the elderly, cognition is measured by several psychometric tests and its association with the risk of dementia is of interest. In a Phase III clinical trial of second-line therapy for malignant pleural mesothelioma, repeated measurements of multi-item patient-reported outcomes were used to predict patient survival. An example of multiple event times is given by a study to investigate the impact of air quality on respiratory symptoms, in which recurrence of respiratory symptoms including runny nose, cough, and sore throat was monitored daily. Addition to recurrent events of the same cause, multivariate survival data are also commonly observed in studies where the events emerge in clusters, for example, twins, families, and different anatomical sites on the same patient, and it is often of interest to assess the association between the response variables and multivariate survival times.