Abstract
The success of the phylogenetic approach within its broad range of potential applications requires the development of powerful inference methods and a clear definition of their conditions for application. The theoretical efforts thus attempted to consider the problem of phylogenetic reconstruction within a statistical framework with the development of methods incorporating sequence evolution on their basic assumptions. In this context, probabilistic methods based on the likelihood function appeared particularly adapted to the analysis of molecular data. These methods based on explicit models of sequence evolution have the advantage to allow the application of a broad range of statistical tests to evaluate various evolutionary hypotheses. The maximum likelihood method profited from many successive improvements aiming at describing as well as possible the processes of biological sequence evolution. This method appears particularly powerful and its desirable statistical properties make it the currently most used method in the fields of molecular evolution and phylogenetic reconstruction.