The use of Bayesian non-parametric (BNP) priors in applied statistical modeling has become increasingly popular in the last few years. From the seminal paper of Ferguson (1973, Annals of Statistics), the Dirichlet Process and its extensions have been increasingly used to address inferential problems in many fields. Examples range from variable selection in genetics to linguistics, psychology, human learning , image segmentation and applications to neurosciences. The increased interest in non-parametric Bayesian approaches to data analysis is motivated by a number of attractive inferential properties. For example, BNP priors are often used as flexible models to describe the heterogeneity of the population of interest, as they implicitly induce a clustering of the observations into homogeneous groups.In the big data era, there is a growing need of models that can describe the main features of large and non-trivial datasets. The information held in these kind of datasets is increasingly easily available to collect through modern networks such as the Internet. This proposal wants to provide flexible priors for explaining such datasets, in particular two research lines will be developed:1. Non-exchangeable BNP priors for modelling the heterogeneity of the data,2. Vectors of Dependent BNP priors for modelling information pooling across units.The successful completion of this research will provide new powerful statistics tools for the analysis of complicated phenomena. New BNP priors will be proposed as well as the application of some recent BNP priors proposed by the principal investigator (Leisen and Lijoi, 2011 Journal of Multivariate Analysis and Leisen, Lijoi and Spanò, 2013 Electronic Journal of Statistics). Specifically, applications of such priors will be developed in the fields of Economics and Genetics.