Supertrees can be used to combine partially overalapping trees and generate more inclusive phylogenies. It has been proposed that Maximum Likelihood (ML) supertrees method (SM) could be developed using an exponential probability distribution to model errors in the input trees (given a proposed supertree). When the tree-­‐to-­‐tree distances used in the ML computation are symmetric differences, the ML SM has been shown to be equivalent to a Majority-­‐Rule consensus SM, and hence, exactly as the latter, it has the desirable property of being a median tree (with reference to the set of input trees). The ability to estimate the likelihood of supertrees, allows implementing Bayesian (MCMC) approaches, which have the advantage to allow the support for the clades in a supertree to be properly estimated. I present here the L.U.St software package; it contains the first implementation of a ML SM and allows for the first time statistical tests on supertrees. I also characterized the first implementation of the Bayesian (MCMC) SM. Both the ML and the Bayesian (MCMC) SMs have been tested for and found to be immune to biases. The Bayesian (MCMC) SM is applied to the reanalyses of a variety of datasets (i.e. the datasets for the Metazoa and the Carnivora), and I have also recovered the first Bayesian supertree-­‐based phylogeny of the Eubacteria and the Archaebacteria. These new SMs are discussed, with reference to other, well-­‐ known SMs like Matrix Representation with Parsimony. Both the ML and Bayesian SM offer multiple attractive advantages over current alternatives.