Subspace clustering is an extension of traditional clustering that seeks to find clusters embedded in different subspaces within a dataset. This is a particularly important challenge with high dimensional data where the curse of dimensionality occurs. It also has the benefit of providing smaller descriptions of the clusters found. In this field, we show that using probabilistic models provides many advantages over other existing methods. In particular, we show that the difficult problem of the parameter settings of subspace clustering algorithms can be seen as a model selection problem in the framework of probabilistic models. It thus allows us to design a method that does not require any input parameter from the user. We also point out the interest in allowing the clusters to overlap. And finally, we show that it is well suited for detecting the noise that may exist in the data, and that this helps to provide a more understandable representation of the clusters found.