Bayesian nonparametric techniques rely on suitable construction of random probability measures. The canonical example is without doubt the Dirichlet process, however in some situations different models are more suitable or preferred. Whereas most available alternatives to the Dirichlet process tend to generalized it in order to overcome certain prediction or fitting drawbacks, some of these issues might be rather solved with simpler models. Here we will review one of these simpler nonparametric

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... priors, which can be seen as generated through a set of ordered weights within a species sampling model representation. We discuss various aspects of these random distributions as well as some of their applications in nonparametric mixtures, covariate or time dependent settings.