This dissertation deals with Bayesian nonparametric statistics, in particular nonparametric mixture models. The manuscript is divided into a general introduction and three parts on rather different aspects of mixtures approaches (sampling, asymptotic, inverse problem). In mixture models, the parameter to infer from the data is a function. We set a prior distribution on an abstract space of functions through a stochastic integral of a kernel with respect to a random measure. Usually, mixture models were used primilary in probability density function estimation problems. One of the contributions of the present manuscript is to use them in regression problems.In this context, we are essentially concerned with the following problems :- Sampling of the posterior distribution- Asymptotic properties of the posterior distribution- Inverse problems, in particular the estimation of the Wigner distribution from Quantum Homodyne Tomography measurements.