  Standard multivariate analysis methods aim to identify and summarize the main
structures in large data sets containing the description of a number of
observations by several variables. In many cases, spatial information is also
available for each observation, so that a map can be associated to the
multivariate data set. Two main objectives are relevant in the analysis of
spatial multivariate data: summarizing covariation structures and identifying
spatial patterns. In practice, achieving both goals simultaneously is a
statistical challenge, and a range of methods have been developed that offer
trade-offs between these two objectives. In an applied context, this
methodological question has been and remains a major issue in community
ecology, where species assemblages (i.e., covariation between species
abundances) are often driven by spatial processes (and thus exhibit spatial
patterns). In this paper we review a variety of methods developed in community
ecology to investigate multivariate spatial patterns. We present different ways
of incorporating spatial constraints in multivariate analysis and illustrate
these different approaches using the famous data set on moral statistics in
France published by Andr\'{e}-Michel Guerry in 1833. We discuss and compare the
properties of these different approaches both from a practical and theoretical
viewpoint.
