Palaeoecologists and palaeobiogeographers are often confronted with large, multivariate data sets, from which fossil communities (assemblages or associations) or faunal provinces are to be recognized. The complex, multidimensional nature of these data sets, the recognition of the enormous variation of communities and environments both in space and time, and the difficulties of dealing with these problems by the human mind, justify the use of multivariate statistical methods in palaeoecology and palaeobiogeography. Concepts and basic procedures of several commonly used multivariated statistical methods of palaeoecology and palaeobiogeography are reviewed in the wider context of quantitative community ecology and biogeography, basic assumptions about data structure and theoretical and practical limitations are discussed. The emphasis is on evaluation of binary similarity coefficients and two multivariate approaches: cluster analysis and ordination. Thirty-nine binary similarity coefficients are evaluated against nine criteria, Jaccard's coefficient of community is found most suitable as a similarity measure between samples under the conditions tested. Algorithmic procedures of cluster analysis, especially the agglomerative hierarchical cluster analysis techniques, and indirect ordinations (particularly polar ordination, principal component analysis, principal coordinate analysis, correspondence analysis, detrended correspondence analysis, and nonmetric multidimensional scaling) are outlined and their applicability to palaeoecological and palaeobiogeographical data is discussed. Where the data are appropriate, an integration of cluster analysis and ordination is suggested to be applied to the same data. © 1993.