Compositional data are necessarily multivariate and multivariate data always consist of intercorrelated variables. This means that the essential information in the data lies mostly in fewer dimensions than the original data and the object is then to identify these important variance-explaining dimensions. Logratio analysis is a variant of principal component analysis, applied not to the original compositional data, but rather to the complete set of logratios, or equivalently the set of centred logratios. The issue of how to weight the compositional parts is important in logratio analysis, since some parts can have higher relative error than others. A compositional data matrix regarded as a set of responses to a set of explanatory variables can be analysed by redundancy analysis to investigate compositional dimensions directly related to these predictors.