This review focuses on the analysis of temporal beta diversity, which is the variation in community composition along time in a study area. Temporal beta diversity is measured by the variance of the multivariate community composition time series and that variance can be partitioned using appropriate statistical methods. Some of these methods are classical, such as simple or canonical ordination, whereas others are recent, including the methods of temporal eigenfunction analysis developed for multiscale exploration (i.e. addressing several scales of variation) of univariate or multivariate response data, reviewed, to our knowledge for the first time in this review. These methods are illustrated with ecological data from 13 years of benthic surveys in Chesapeake Bay, USA. The following methods are applied to the Chesapeake data: distance-based Moran's eigenvector maps, asymmetric eigenvector maps, scalogram, variation partitioning, multivariate correlogram, multivariate regression tree, and two-way MANOVA to study temporal and space-time variability. Local (temporal) contributions to beta diversity (LCBD indices) are computed and analysed graphically and by regression against environmental variables, and the role of species in determining the LCBD values is analysed by correlation analysis. A tutorial detailing the analyses in the R language is provided in an appendix.