  The idea of a multiverse -- an ensemble of universes -- has received
increasing attention in cosmology, both as the outcome of the originating
process that generated our own universe, and as an explanation for why our
universe appears to be fine-tuned for life and consciousness. Here we carefully
consider how multiverses should be defined, stressing the distinction between
the collection of all possible universes, and ensembles of really existing
universes that are essential for an anthropic argument. We show that such
realised multiverses are by no means unique. A proper measure on the space of
all really existing universes or universe domains is needed, so that
probabilities can be calculated, and major problems arise in terms of realised
infinities. As an illustration we examine these issues in the case of the set
of Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) universes. Then we briefly
summarise scenarios like chaotic inflation, which suggest how ensembles of
universe domains may be generated, and point out that the regularities which
must underlie any systematic description of truly disjoint multiverses must
imply some kind of common generating mechanism. Finally, we discuss the issue
of testability, which underlies the question of whether multiverse proposals
are really scientific propositions.
