The research work presented in this manuscript is of algorithmic kind: it is mainly composed of polynomial, fixed parameter and approximation algorithms, while hardness results are also mentioned.<br /> <br />This work is about building and comparing labelled trees. These objects find application in different areas, but notoriously in phylogenetics, where they represent evolutionary relationships of organisms or sequences.<br /><br />Most of this work can be considered as investigating solutions to so-called \emph{supertree} problems. Supertrees are large trees built by a dynamic programming approach from smaller trees. For instance, the latter are gene trees from which a comprehensive tree on many living species is to be built, such as the \emph{Tree of Life}. <br /><br />First definitions are introduced, then a part of the manuscript is dedicated to quartet tree building methods. The next part details tree comparison methods, mainly variants of the maximum agreement subtree method. Next follows a part on supertree problems in all generality. <br />The manuscript ends with a report of the research plan for the next few years. <br /><br />Several journal papers illustrating the material described in this manuscript are adjoined in appendix.