  Clustering is an important task in many areas of knowledge: medicine and
epidemiology, genomics, environmental science, economics, visual sciences,
among others. Methodologies to perform inference on the number of clusters have
often been proved to be inconsistent, and introducing a dependence structure
among the clusters implies additional difficulties in the estimation process.
In a Bayesian setting, clustering is performed by considering the unknown
partition as a random object and define a prior distribution on it. This prior
distribution may be induced by models on the observations, or directly defined
for the partition. Several recent results, however, have shown the difficulties
in consistently estimating the number of clusters, and, therefore, the
partition. The problem itself of summarising the posterior distribution on the
partition remains open, given the large dimension of the partition space. This
work aims at reviewing the Bayesian approaches available in the literature to
perform clustering, presenting advantages and disadvantages of each of them in
order to suggest future lines of research.
