Repeated observation of multiple outcomes is common in biomedical and public health research. Such experiments result in multivariate longitudinal data, which are unique in the sense that they allow the researcher to study the joint evolution of these outcomes over time. Special methods are required to analyse such data because repeated observations on any given response are likely to be correlated over time while multiple responses measured at a given time point will also be correlated. We review three approaches for analysing such data in the light of the associated theory, applications and software. The first method consists of the application of univariate longitudinal tools to a single summary outcome. The second method aims at estimating regression coefficients without explicitly modelling the underlying covariance structure of the data. The third method combines all the outcomes into a single joint multivariate model. We also introduce a multivariate longitudinal dataset and use it to illustrate some of the techniques discussed in the article.