In this document, I present various contributions to hidden Markov models on graphs and more generally, to the statistical analysis of graphical data, with a particular focus on tree graphs. In a part following an introduction, three main types of problems in tree analysis are exposed: hidden Markov tree models to predict tree shapes and perform vertex segmentation, edit distances to perform clustering at whole-tree scale and multiple change-point detection on trees. Then some more detailed focus is given to multivariate count modelling, which is one of the main problem to be solved in hidden Markov tree estimation. This is addressed using the theory of probabilistic graphical models. A presentation of three specific contributions to hidden...