After an introduction to the notion of an exchangeable random partition, we continue with a more detailed discussion of the Ewens process and some of its antecedents. The concept of an exchangeable cluster process will be described, the main example being the Gauss-Ewens process. Some applications of cluster processes will be discussed, including problems of classification or supervised learning, and cluster analysis (unsupervised learning). A second type of probabilistic model based on point processes is also described. By contrast, which the Gauss-Ewes cluster process, the domain associated with each class is more diffuse and not localized in the feature space. For both models, the classification problem is interpreted as the problem of computing the predictive distribution for the class of a new object having a given feature vector. In one case, this is a conditional distribution given the observed features, in the other a Papangelou conditional intensity.